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Natural Philosophy, 





Professor of the Natural Sciences and Astronomy in Lake Forest 
University, Lake Forest, Illinois. 








This Natural Philosophy has been written for a text-book 
for classes that have no further acquaintance with the 
Mathematics than simple equations and the properties of 
the square and the parallelogram. It is the result of many 
years experience in teaching the subject, and the author 
has tried to present the principles and discussions in such 
a form as to be readily comprehended by the student. His 
experience has been that in the use of many text-books 
upon this subject, a large part of the teacher's time is em- 
ployed in explaining the language of the text to the pupils, 
since not only are the ideas of the science new to them, 
but these ideas are so expressed that the very words are 
met for the first time. 

Recollecting that most students begin their acquaintance 
with the vast field of Natural Science with this branch, 
an effort has been made to use familiar language, as far as 
possible, so avoiding too great a transition in their work. 
The love of science should be developed from the outset. 
The definitions, especially, have been prepared with an eye 
to brevity and perspicuity. 

Since the principles and laws of this science are deduced 
from experiments, the usual order pursued in the following 
pages has been to describe the apparatus used and the ex- 
periments performed before introducing the laws which 
result from them. This aids in teaching the student to 
observe and experiment for himself. 

Problems illustrating and applying the principles have 
been introduced throughout Mechanics, and to some extent 
under the Undulatory Forces, and .these have been given 


both in the metric system and in the common system of 
weights and measures. They usually refer to the section 
where the principle upon which the solution depends is 
discussed. It is hoped that teachers will add to these in 
such a way as to develope the habit of applying the prin- 
ciples to surrounding phenomena. 

The forces which act upon bodies as wholes have been 
treated first because most pupils pass more readily to the 
phenomena of undulations after they have become familiar 
with the former. So too, the Undulatory Forces are dis- 
cussed as a whole of which Light, Heat, and Electricity 
make a part. This seems to render the idea of conserva- 
tion less difficult to grasp. 

The author desires to express his obligations to Prof. 
George C. Merrill, Peabody Instructor in the Natural Sci- 
ences at Phillips Academy, Andover, Mass., for his kindness 
in reading the manuscript, and for his valuable suggestions. 
The various pieces of Apparatus required for full illustra- 
tration can be found with Messrs. E. S. Ritchie & Sons, 
Boston, Mass., who kindly allowed the use of a large 
number of their cuts in making the plates. Special atten- 
tion is invited to the methods of illustrating wave motion. 

For a more complete discussion of the subjects, the stu- 
dent is referred to such works as Deschanel's Natural Phi- 
losophy; Atkinson's Ganot's Physics; Pynchon's Chemical 
Forces; Cooke's Chemical Pl^sics; Tyndall's Heat a Mode 
of Motion, and On Sound; Noad's Text-Book of Electric- 
ity, and Tait's Recent Advances in Physical Science. 

Lake Forest, III., Jan. 1881, 



Chapter I. — General Principles— Definitions — States of 

Matter— Indestructibility. - - - 1— i 

Chapter II.— Properties of Matter— Defined and Clas- 
sified. Section I. Universal Properties, named and 
defined. Section II. Specific Properties. - - 4—11 

Chapter III.- Attraction. Section I. Molecular Attrac- 
tion — Friction — Capillarity — Osmose. Section II. 
Gravitation — 'Centre of Gravity • — Equilibrium — The 
Balance— Laws of Falling Bodies— The Pendulum. 11 — 33 


Chapter I. — Impulsive Forces. Section I. Movements 

of Forces. Section II. Composition of Forces. - 34—40 

Chapter II. — Undulatory Forces. Longitudinal Vi- 
brations — Transverse Vibrations — "Water Waves. - 40 — 42 


Chapter I. —Mechanics op Solids. Sec. I. Simple Ma- 
chines — Cord — Lever and Combinations — Centrifugal 
and Centripetal Forces — Inclined plane. Section II. 
Strength of Materials— Piinciples of Frames. - - 43—59 

Chapter II. — Mechanics op Liquids. Section I. General 
Properties. Section II. Specific Gravity, end its de- 
termination. Section III. Hydrostatics — Pascal's 
Law — Press — Reservoirs. Section IV. Hydraulics — 
Jets— Wells— Ram— Water Wheels. - - - 59—80 

Chapter III. — Mechanics op Gases — Expansibility and 
Compressibility. Section I. Tbe Atmosphere — Air 
Pump — Balloons. Section II. Barometers. Section 
III. Boyle's Law — Manometers. Section IV. Appa- 
ratus depending upon gases. - - - 81 — 98 

Division I. — General Principles. 
Chapter I. — Laws of Motion. Section I. Laws of In- 
tensity — Means of Strengthening. Section II. Ve- 
locity of Sound — in Gases — Liquids — Solids. - 102 — 107 
Chapter II. — The Effect of Surfaces. Section I. Re- 
fraction. Section II. Reflection— Echo. - - 107 — 113 
Division II. — Applications. 
Chapter I. — Musical Sounds. Section J. No, of Vihra* 


tions. Section II. Theory of Music. Section III. 
Musical Instruments— Cords — Pipes. - 114—126 

Chapter II. — Acoustic Figures. Sec. I. Plates and 
Membranes. Section II. Optical representation of 
Vibrations. - - - - - - 126—131 

Chapter III. — Vibrating Instruments. Section I. Tel- 
ephone — Photophone. Section II. — Phonograph. 131 — 134 

Chapter I. — Effects of Heat. Section I. Expansion — 
Coefficients — Thermometers. Section II. Fusion and 
Solidification. Section III. Vaporization — Boiling — 
Cooling by evaporation — Ilygrometry — Rain and 
Snow. Section IV. Spheroidal Condition. - - 136—159 

Chapter II.— Methods of Moving. Section I. Conduc- 
tion — in solids — in liquids and gases. Section II. 
Convection. Section III. Badiation. Section IV. 
Sources of Heat — Chemical — Mechanical. - - 160 — 170 

Chapter III. — Specific Heat. Section I. Determina- 
tion. Section II. The Steam Engine. - 171—177 

Chapter I. — Sources and Movement of Light. Sec- 
tion I. Sources of Light — Shade and Shadow — Pho- 
tometry. Section II. Movement of Light. - 179—187 

Chapter II. — Interception of Light. Section I. Re- 
flection — Irregular — Regular — Mirrors. Section II. 
Refraction — Laws — Prism — Spectrum — Lenses. - 188 — 206 

Chapter III.— Optical Instruments. Section I. Tele- 
scope. Section II. Microscope. Section III. Camera 
and Lantern. Section IV. Spectroscope. Section V. 
Rainbow. Section VI. Eye. - - - 206—217 

Chapter IV. — Undulatory Theory. Section I. Inter- 
ference. Section II. Double Refraction. Section III. 

Polarization. 217—223 


Chapter I. — Magnetism. Section I. Magnets — Ampere's 
Theory. Section II. Needle — Compass. Section III. 
Magnetization. - - - - - 224—234 

Chapter II. — Frictional. Section I. Fundamental Phe- 
nomena. Section II. Laws — Intensity — Distribution 
— Density. Section III. Induction — Condenser. Sec- 
tion IV. Machines. Section V. Effects — Mechanical 
— Heating — Luminous — Magnetic. Section VI. Thun- 
der Storm. ----__ 234—256 

ChapterIII. — Voltaic. Section I. Current. Section II. 
Batteries — Smee's — Daniell's — Bichromate — Grove's — 
BuDsen's— Pile. Section III. Effects— Magnetic— Tel- 
egraph — Heating — Luminous — Chemical. - - 256 — 272 

Chapter TV. — Induced. Section I. Production of the 
Current. Section II. Effects— Physiological— Heating 
—Luminous. "" ■ - B - - - - 272—281 

Natural Philosophy, 




1. Physics treats of matter and the forces that act upon 
matter without changing its nature. Forces that produce 
a change in its nature are considered in Chemistry. 

2. Matter is anything that occupies space. It reveals 
its existence and properties by affecting our senses. A 
separate portion of matter is termed a body. Investigations 
in Physics determine the properties of bodies, and then 
reasoning extends these results to all matter. 

3. Atoms and Molecules. Bodies are made up of small 
masses called molecules. These do not touch each other, 
at least on all parts of their surface, and are constantly in 
motion. Their size and shape are unknown, though some 
consider them spherical, and others ring shaped; but no 


molecule can be divided without changing the nature of 
the body. Molecules themselves are made up of atoms. 
An atom is a portion of matter that cannot be divided. 
The difference between an atom and a molecule is that an 
atom can contain but one elementary substance, while a 
molecule is a collection of atoms, and may contain several 

4. A body that is not known to contain more than one 
kind of matter is called an element. The number of ele- 
ments at present recognized is sixty-six. Most of these 
are rare, and known only to the Chemist, while some eight 
or ten make up the principal portion of the earth, at least 
to the depth to which men have been able to penetrate. 

5. Force. Whatever produces, or tends to produce mo- 
tion, is called a force. When applied to the exterior of 
bodies so as to act upon them as single masses, forces 
produce change of position, and are called external forces. 
When they act between the molecules of a body, they are 
molecular forces and determine the three states of matter. 

6. The three states of matter.* Two opposing forces, 
or sets of forces, act upon the molecules of all bodies, an 
attractive and a repellent. The first tends to bring the 
molecules nearer to each other, and acting alone, would 
bring them all into contact; the second tends to separate 
them, and unopposed would remove them to an infinite 
distance from each other. Heat is the principal, perhaps 
the only repellent force. According to the relative strength 
of these two forces, matter may take either of three states, 
Solid, Liquid, or Gaseous. 

7. A Solid retains its molecules in the same relative 
position; as ice, granite, iron. Solids retain their shape 
permanently, and offer considerable opposition to any 

*Eecent experiments made by Prof. Crookes seem to indicate a fourth state, 
named by him Eadiant. These investigations require further confirmation. 


attempt to modify their form. In them, the force of at- 
traction much exceeds repulsion. 

8. A Liquid takes the form of any containing vessel, 
and a very slight external force may change the relative 
position of its molecules; as water, mercury, or melted 
iron. The two forces are nearly balanced, the attractive 
slightly exceeding the repellent, as is shown by the spher- 
ical form of small masses, as rain drops. 

9. A Gas constantly struggles to occupy a greater vol- 
ume. The repellent force exceeds the attractive, and sends 
the molecules from each other in straight lines until stopped 
by some external force; as steam, air, or vapor of iron. 
The molecules of a gas constantly move with inconceivable 
rapidity, and hence any gas will expand and fill the entire 
volume of a containing vessel. 

10. All elementary substances, and those compounds 
which are not decomposed at too low a temperature, can 
be made to take either of these states at will, by varying 
the amount of heat acting upon them. Water is a familiar 
example. At the temperature of 0°, it is a solid, ice.* 
Heated, it becomes a liquid. Heat the liquid to 100°, and 
it becomes an invisible gas. 

11. A Phenomenon is any change in a body either ex- 
ternal or molecular: as the fall of an apple, the swinging 
of a string and attached weight, or the boiling of water. 

12. A Physical Law is the relation between a phenom- 
enon and its cause, and it also applies to similar phenomena. 
Thus the relation between the fall of a stone and the force 
which made it fall, is called the law of gravitation. 

13. A Theory is the collection of all the laws relating 
to a single subject into one truthful whole; as the theory 

*The Centigrade scale is used in this work. 



of light. It must correctly explain all possible phenomena 
belonging to that subject. Until it is proved to do this, 
it is merely an hypothesis, though often called a theory. 

14. Indestructibility. Careful experiments with the 
balance have proved that the application of the various 
forces can cause matter to change its form, but can neither 
increase nor diminish its amount. Thus ice may melt, 
and the resulting water boil, but the weight of the steam 
produced is the same as that of the water or ice. So too, 
if it be decomposed into its constituents, oxygen and 
hydrogen, the weight of the gases will equal that of the 
water. In like manner, the form of the various forces can 
be changed. Heat can take the place of the motion of a 
falling body, or the reverse, but the total amount of energy 
will remain the same. So neither force nor matter can be 
changed in amount, except by the Creator. 



15. Bodies produce various effects upon our senses de- 
pending upon the substances of which they are composed. 
The causes which produce these various effects are termed 
the Properties of Matter. They are of two kinds, Univer- 
sal, that is belonging to all matter; and Specific, belonging 
only to certain bodies. Thus a block of wood, a glass of 
water, and a rubber ball, all occupy a definite portion of 
space, and can be moved in space, universal properties; but 
their color and taste differ, specific properties. 

Section I.— -Universal Properties. 

16. The Universal Properties of matter are Extension, 


Impenetrability, Inertia, Divisibility, Porosity, Compressi- 
bility, Elasticity and Mobility. The first three are essential 
to our idea of matter. 

17. Extension is the property of occupying space. 
Every body occupies a limited portion, and hence has 
three dimensions — length, breadth and thickness. The 
surface is the outside of a body, and every body has a cer- 
tain definite form or figure. Its volume is the amount of 
space it occupies. The extent of surface belonging to a 
body depends upon the form and volume. 

18. Extension is measured in terms of some arbitrary 
standard. That in common use is the yard, but in all 
philosophical calculations, and in many of those of common 
life, the ten-millionth part of a quadrant of the are of a 
meridian of the earth is adopted and called a metre* This 
is divided and subdivided into tenths, hundredths, etc. 
The unit of surface is the square of the unit of length, 
and the unit of space is its cube. The unit of weight 
is a cubic centimetre of distilled water, at the temperature 
of 4°, and is called a gramme. These units should be 
carefully remembered, and with them the unit of time, one 

19. Impenetrability is the property of matter which 
prevents two portions from occupying the same space at 
the same time. 

20. The impenetrability of solids demands no proof. Apparent 
exceptions, as driving a nail into wood, result from the displace- 
ment of the molecules. The impenetrability of liquids is shown 
by placing a solid in a vessel filled to the brim with water : some 
of the water is displaced. An inverted glass vessel thrust into 
water shows the impenetrability of gases, as the water does not 
rise to fill the vessel. 

* A mistake was made in the measurement of this quadrant, hence the 
metre is only an approximation. 


21. Inertia keeps a body in its present state, whether of 
rest or of motion. It is a purely negative property, and 
because of it, any change in position or state must be 
caused by the application of some external force. Thus a 
ball of lead at rest in the hand does not fall, when the 
hand is removed, because of any inherent property, but be- 
cause of the force of the earth's attraction. 

22. The inertia stand, Figure 1, furnishes a convenient means 

of proving the property. A card is 

placed upon a pillar of wood, and a ball 

balanced upon the card exactly above the 

pillar. By means of a spring, a smart 

blow is struck upon the card, driving it 

out, while the inertia of the ball prevents 

that from moving. So suddenly moving 

g * lm a stick which has a drop of water upon 

one end, leaves the drop of water behind, and proves the inertia 

of liquids; while fanning shows the inertia of gases. 

23. Applications. Many common phenomena are due to 
inertia. In throwing a ball, the hand gives motion to the 
ball, and its inertia carries it forward after leaving the 
hand. A person runs a short distance before leaping a 
ditch, that the inertia of the body may assist the muscles. 
The athlete will place an anvil upon his chest and allow a 
heavy blow to be struck upon it, because the inertia of the 
anvil distributes the force of the blow before it reaches the 
chest. In leaping from a moving carriage or railway car, 
the motion of the feet is suddenly stopped, while the 
inertia of the body carries it forward. Railway accidents 
are due to inertia. The engine is suddenly stopped, 
while the inertia of the cars drives them forward, crushing 
one into another. The inertia of a moving hammer ena- 
bles it to overcome the friction of the nail against the 
wood. Pestles, stamps, and fly wheels are other applica- 
tions of inertia. 

24. Newton's First Law of Motion results from inertia. 


It may be thus expressed: "If a body be at rest, it will 
remain at rest; if it be in motion, it will continue to move 
in the same direction and with the same velocity.' 1 

25. Divisibility is the property which allows a body to 
be separated into parts. By mechanical and chemical 
operations, this division and subdivision may be continued 
until the ultimate atoms are reached. But when the mol- 
ecules are separated into their constituent elements, the 
nature of the body is changed. The means of mechanical 
division at our command are so imperfect as to fail long 
before the molecules are reached. 

26. Numerous examples of the extreme divisibility of 
matter may be given. Gold can be beaten so thin that 
more than five hundred leaves are required to equal a cen- 
timetre in thickness. The gilt wire used in embroidery 
has a thickness of gold of about an eight-thousandth of a 
millimetre. Yet this can be cut into lengths no greater 
than the thickness, and each piece be seen by the aid of a 
microscope. The diameter of human blood discs does not 
much exceed the tenth of a millimetre. Dissolve a bit of 
aniline red not larger than the head of a pin in 10 c. c. of 
alcohol, and a single drop placed in a litre of water will 
color the whole perceptibly. A grain of musk placed in a 
room will diffuse a marked odor for years without losing 
weight appreciably. 

27. Porosity is the property in virtue of which spaces 
exist between the molecules of a body. The spaces are 
called pores. They are of two kinds, physical and sensible. 

28. Physical Pores are spaces between the molecules so 
small that molecular forces act the same as though they 
did not exist. All bodies contain such pores. They reveal 
their existence in most bodies by the fact that the bodies 
contract with the loss of heat. If the molecules touched 


each other, and pores were absent, contraction would be 
impossible. Liquids show their porosity by dissolving 
solids, as sugar in water, without increasing the volume of 
the liquid. So too, many liquids can be mixed, as water 
and alcohol, and the mixture occupies less space than the 
sum of the separate liquids. Gases are so porous that if a 
vessel be filled with one gas, another may be placed in the 
vessel the same as though the first was not there. Even 
bodies that do not readily show their pores can be expanded 
by heat, and since this force cannot change the size of the 
atoms, it increases their distance from each other. 

29. Sensible Pores are openings in bodies that appear 
to the eye. Thus the vacant places in a sponge, where the 
water moved in life, are sensible pores. So are the places 
in wood where the sap moved. 

30. Compressibility is the property which allows bodies 
to be diminished in volume by the application of external 
force. It is the direct result of porosity. All bodies are 
compressible to a certain extent. Gases are the most, and 
liquids the least compressible in proportion to the force 
exerted. With moderate pressures, gases lose volume very 
rapidly, and the diminution of volume can continue until 
they take the liquid state. Liquids were formerly regarded 
as incompressible, but the piezometer* clearly proves that 
they are slightly compressible. The compressibility of 
solids varies very much. Cloth, paper, cotton and wood 
are among the most compressible. Metals are quite com- 
pressible. But there is a limit beyond which the increase 
of pressure reduces the body to a powder. 

31. Elasticity causes bodies to resume their original 
form when a distorting force has been removed. Were 
the elasticity perfect, bodies would exactly regain their 

*See Section 212. 


original form. Since in gases the repulsive force is stronger 
than the attractive, their elasticity has no limit. Liquids 
also appear to he perfectly elastic. But no known solid is. 
Though all solids show the property to a certain extent, 
no one ever exactly regains its original form. After a 
short time, batting the ball destroys its spherical shape. 
Glass, ivory, iron and ice are among the most elastic solids. 

32. Elasticity may he developed by compression, by 
traction or pulling, by flexion or bending, or hy torsion 
or twisting. The first belongs to all states of matter, the 
others only to solids. 

33. Mobility is the property which allows a body to 
change its position in space. Rest and motion are both 
absolute and relative. Absolute rest is continuance in the 
same point of space, and is unknown in nature. Relative 
rest is continuance in the same position in relation to sur- 
rounding objects, as a book placed upon the table is at rest 
in relation to the objects of the room, though all are sub- 
ject to the common motion of the earth. So the passenger 
sitting in the railway car is at rest in regard to the train 
though moving rapidly forward. 

34. Absolute Motion is motion in regard to some fixed 
point: relative, in regard to moving objects. A person 
sitting in a boat is at rest in relation to the boat, but in 
motion in relation to the neighboring shore : but if he were 
to walk toward the stern at the same rate that the boat 
moves forward, he would be in motion in relation to the 
boat, but at rest in relation to the shore. 

Section" II. — Specific Properties. 

35. The most important specific properties of matter are 
Hardness, Tenacity, Ductility, Brittleness, Malleability, 
Transparency, and Color, Taste and Odor. 


36. Hardness is the property which causes a hody to 
resist a scratch upon its surface. Bodies are hard or soft 
in comparison one with another, the harder being the one 
which will scratch the other. On this basis, a scale of 
hardness has been formed with the diamond at one end. 
(See Table I.*) 

37. Tenacity is the property which resists a force acting 
in the direction of the length of a body to separate its 
molecules. Its strength has been determined in many 
substances, by making cylinders of them and finding the 
weight required to break them. It is proportional to the 
breaking weight, and also to the transverse section. In 
bodies whose texture varies in different directions, the 
tenacity is greatest in the direction of the fibres. 

38. Ductility is the property which allows a body to be 
drawn into a wire. Soft bodies require little force to pro- 
duce this change; the resins and glass need to be heated, 
when they can be spun into fine threads; metals, as iron 
and copper, require the draw plate. The tenacity of the 
more ductile metals is increased by drawing them into 
wires, because the fibres are then placed in the same direc- 
tion, and a transverse strain is impossible. Platinum is 
the most ductile metal. 

39. Malleability allows metals to be rolled or hammered 
into thin plates. Gold is the most malleable under the 
hammer and may be beaten into leaves not exceeding one- 
fiftieth of a millimetre in thickness. 

40. Brittleness renders a body capable of being easily 
pulverized. It is usually connected with hardness, and the 
brittleness of a body usually increases as the hardness, but 
not always. Tempering, the sudden cooling of a heated 
solid, generally increases both the elasticity and the brit- 

*End of the Volume. 


tleness. Thus hardened steel is much more elastic than 
that which has not been tempered, but it is at the same 
time more brittle. 

41. Transparency is the property which allows light or 
heat to pass through a bod}'.* No substance allows all 
the force to pass, but bodies of different substances, and of 
the same thickness, vary much. Thus light will readily 
pass through glass of considerable thickness, but a very 
thin plate of iron will intercept it entirely. So with heat, 
but the substances which intercept heat are not the same 
as those which intercept light. Thus rock salt will trans- 
mit more heat than any other substance, and a solution of 
iodine stands next to it. But salt will allow light to pass 
nearly as well as the heat, while the solution of iodine is 

42. Color, Taste and Odor are the properties possessed 
by bodies of exciting the corresponding sensations when 
brought in contact with the appropriate nerves. Though 
the manner in which the sensations arise cannot be ex- 
plained, each body certainly possesses some property which 
is peculiarly its own, and gives rise to its appropriate sen- 
sation, whether of color, taste, or smell. 



43. Attraction is the force which tends to diminish the 
distance between bodies. When it acts between molecules, 
it is molecular attraction; when between masses as wholes, 

♦Bodies which allow heat to pass readily are called Diathermanotis. The 
property seems to be identical with Transparency because of the identity of 
light and heat. 


it is termed gravitation. Electricity as an attractive f orct 
acts by polarization of the molecules. 

Section I. — Molecular Attraction". 

44. Cohesion is the attraction between molecules of the 
same substance. It varies, I, according to the state of 
the body, since heat opposes it. Hence it is strongest in 
solids, weaker in liquids, and is entirely overcome in gases. 
It varies, II, according to the nature of the body, being 
usually strongest in those which are the most dense, but 
not invariably. It varies, III, according to the arrangement 
of the molecules. Thus, moderately tempering steel makes 
it stronger; and generally cohesion is much greater in the 
direction of the fibers than in any other direction. Hence 
the ductile metals are much strengthened by drawing them 
out into wires. 

45. The special properties of solids result from cohesion. 
Several of these have been already mentioned.* Elasticity 
of Traction, Torsion, and Flexion remain to be treated. 

46. Elasticity of Traction. When a rod or wire is 
stretched, the force which it exerts in opposition to the 
stretching is the Elasticity of Traction. Each substance 
has a limit beyond which it gradually "yields to the force, 
the molecules take new positions, and the body is finally 

47. When the limit is not exceeded, the elasticity is 
governed by the following laws: 

I. Bods and toires resume their original length ivhen the 
force of traction is removed. 

II. The elongation is proportional to the force, and to the 
length of the body. 

♦See Properties of Matter, Section 15. 



III. In bodies of the same substance and length, the elon- 
gation is inversely proportional to the area of a cross section. 

48. Elasticity of Torsion. A heavy weight supported 
by a rod or wire, comes to rest in a certain position. If 
now it be twisted, the force applied is called the force of 
torsion; the distance it is moved, the angle of torsion; and 
the resistance offered, the elasticity of torsion. 


Coulomb's Torsion Balance, Figure 2, 
shows Elasticity of Torsion. A is the 
point of support, B the weight with an 
attached index, and C D a graduated cir- 
cle to show the angle, placed a little below 
the weight B. When the weight B is 
twisted by any force, and the force re- 
moved, the elasticity of A B brings the 
index back to its original position. But 
its inertia carries it just as far to the 
other side, when the elasticity again 
stops it, to repeat the oscillation. 

Were the elasticity perfect, all the 
oscillations would be equal; but in 
fact, the angle constantly diminishes, 
and after a short time the body comes 
to rest. 

Fig. 2. 

The laws governing the oscillations 
determined by the apparatus are: 

I. The times of the oscillations are equal. 

II. The angle of torsion is proportional to the force em- 

III. With the same force, the angle of torsion is propor- 
tional to the length of the sustaining wire or rod. 

IV. The angle is inversely proportional to the fourth pow- 
ers of the diameters. 


4:9. Elasticity of Flexure. The resistance which a body 
offers to bending is termed Elasticity of Flexure. This is 
of great practical value, and is employed in carriage 
springs, bows, watch springs, etc. It is increased by hard- 
ening or tempering, as in steel, and is diminished by an- 

50. Hardening a metal generally consists, in heating the 
body and cooling it suddenly. It usually increases the 
elasticity, and at the same time renders the body more 
brittle. Copper, however, is softened by the same process. 
Annealing is the reverse of hardening, and consists in heat- 
ing a body and cooling it slowly. 

51. The Cohesion of Liquids is shown by the spherical 
form of small drops. In large masses, the weight over- 
comes the cohesion, and the liquid assumes the shape of 
any containing vessel. 

52. Cohesion once overcome can not usually be renewed. 
Some solids, however, can be welded, a process which con- 
sists in heating the body, usually with a flux, nearly to its 
melting point and hammering the molecules into contact. 

53. Adhesion is the attraction between molecules of dif- 
ferent substances. Usually it is less intense than cohesion, 
but not always. 

54. I. Adhesion between Solids. When a solid is brought 
in contact with another of different material, and no air 
intervenes, the molecules attract each other. They fre- 
quently hold together with a force equal to that exerted 
between molecules of the same substance. Thus glue be- 
tween two pieces of wood holds them by adhesion, and the 
wood breaks before it separates from the glue. 

55. Friction results partly from the adhesion of solids 



to solids, and partly from the roughness of the surfaces of 
all solids. It is of two kinds, Sliding Friction, and Boiling 

56. Sliding Friction is the resistance to the motion of 
one solid over another in opposition to adhesion and to 
the roughness of the surface. The latter compels the 
upper body to move away a distance equal to the largest 
prominences upon the surfaces. 

57. Thus if a smooth block C, 
Fig. 3, be moved over the table D E, 
the block adheres to the table, and 
is raised a little from its surface. By 
means of this apparatus, the fol- 
lowing laws of sliding friction have 
been determined: 

I. Friction at starting is 

Fig> 3t greater than between the same 

bodies in mot ion, and it increases 

with the length of time the bodies have been in contact, until 

they have been so about fifteen days. 

II. Tlie friction is proportional to the pressure. 

III. TJte friction is independent of the extent of surface 
in contact, and of the velocity. 

IV. The friction is greater between surfaces of the same 
materials than between different substances. 

58. Rolling Friction is the friction of a body when 
rolling along another. It is generally much less than 
sliding friction. Hence whenever possible, sliding friction 
is changed by wheels to rolling. Both are diminished by 
using lubricants, as oil, since these partially fill up the 
roughnesses of the surfaces in contact. 



59. II. Adhesion of Solids and Liquids is seen by 
the wetting of the hand when plunged into water. Its 
power may be determined by the following experiments, 
Fig. 4: 

Suspend a glass or metal plate 
from one arm of a balance, and 
place sufficient ■weights in the 
pan on the other arm to balance 
the plate. Now bring the un- 
der surface of the plate into 
contact with water. Several 
grammes will be required to 
remove it, and when separated, 
Fig. 4. the under surface of the plate 

is wet. So the weights added become the measure of the cohe- 
sion of the water, while the adhesion of the plate to the water is 


Capillarity results from the adhesion of solids and li- 
quids: but from its importance, it is treated as a separate 

60. III. Adhesion of Solids to Gases is shown by the 
bubbles of air that quickly appear when a smooth metallic 
plate is plunged into a vessel of water. Its power is con- 
siderable, and it is difficult to put two substances together 
so closely that a film of air shall not intervene. Hence 
when bodies are glued, after putting on the glue, pressure 
is applied that the air may be forced out. This is the prin- 
cipal reason why cohesion can so rarely be renewed when 
once overcome. 

61. IT. Adhesion of Liquids to Liquids is shown by 
diffusion. If two different liquids whose adhesion for 
each other equals or exceeds the cohesion, are placed in a 
vessel together, after a time determined by the strength of 
adhesion, they are found equally mixed. 



Thus if a vessel of water, A B, Fig. 5, col- 
ored blue by a little litmus, be taken, and some 
sulphuric acid, which is nearly twice as heavy 
as water, be poured into the bottom by means 
of the thistle tube C, in a short time the water 
turns red. This shows that the acid has risen, 
or diffused, through the lighter water. 

62. T. Adhesion of Liquids and Gases 

is shown by the solution of gases in 
water. Thus, if a vessel of water that 
has been exposed to the air be heated, bubbles of air are 
seen rising to the surface. These were previously in solu- 

63. Solution, whether of solids, liquids or gases, results 
from adhesion. Water is the usual solvent, and frequently 
dissolves salts without increase of volume, because the dis- 
solved substance occupies the pores. Solution is usually 
attended by change of temperature, the solution becoming 
colder than the water. Thus sugar and common salt are 
dissolved by water. 

64. Capillarity. The change of level when a solid is 
placed in a liquid is called Capillarity, because the phe- 
nomenon is best exhibited by very fine tubes. It presents 
two distinct cases; when the liquid is capable of wetting 
the solid, and when it is not. The first is Capillary Attrac- 
tion: thesecon 1 , Capillary Repulsion. 

65. Capillary Attraction. If a 

a plate of glass C, Figure 6, is 
plunged into a vessel of water 
A B, the water rises on the sides 
of the plate and forms a curve. 

Fig. 6. The rise of the liquid is 

caused by the attraction between its molecules and those of 

N. P. 2. 



the solid, and it is a case of adhesion of a liquid to a solid. 
The height to which the liquid will rise depends upon the 
nature of the substance, and in every case where the cohe- 
sion of the liquid is not overcome, is such that the weight 
of the liquid raised above the level equals the attraction of 
the solid for the liquid. 

66. If a second plate of the 
same substance, Fig. 7, is placed 
in the liquid, the liquid will 
rise around that in the same 
way as around the first. If the 
two plates are brought so near 
that each attracts some of the 
molecules raised by the other, 
Fig. 7. the liquid will rise higher be- 

tween them, and the upper surface of the liquid will be concave. 


67. Capillary Repulsion. If a 

glass plate F, Fig. 8, be placed 
in a liquid whose cohesion is 
greater than the attraction of 
the glass, e. g., mercury, the 
liquid will be depressed. 

Fig. s. This last is Capillary Be- 

The surface of the liquid becomes convex. 

68. Laws of Capillarity. The following laws have been 
demonstrated theoretically: Gray-Lussac has also shown 
their truth experimentally. 

I. A solid raises or depresses a liquid according as it 
is moistened or not. 

II. In different tubes placed in the same liquid, the eleva- 
tion varies inversely as the diameter of the tube. 

III. Tubes elevate a liquid twice the distance of plates 
ivhose distance apart equals the diameter of the tubes. 



IV. The elevation varies with the liquid, and the tempera- 
ture, but is independent of the thickness of the tube. 

69. These laws apply to both forms of capillarity. 

70. Experiments upon Capillarity. Attraction is 
best shown by placing a series of tubes of differ- 
ent diameter, side by side in a vessel of water, 
colored by a little red aniline. See Fig. 9. The 
water stands in the tubes in the inverse order of 
their diameter. 

71. The same tubes placed in a vessel of mer- 
cury show repulsion. See Fig. 
10. In the first case the surface 
of the liquid is concave: in the 
second, convex. 

Fig. 9. 

72. Two plates placed a little 
distance apart raise the water 
between them, and a tube of 
Fi £- 10 - the diameter of the distance 

"between the plates placed beside them raises the water twice as 
high as the plates, thus showing the law. If 
now the plates are placed with one edge touch- 
ing while the other is separated a little, Fig. 
if the water rises to the top where they touch, 
and falls away in a curve, forming the equilat- 
eral hyperbola. 

73. Results of Capillarity. The oil in 

Fig. n. lamps is raised to the flame by the capil- 

lary action of the wick. A towel with one end in water 
quickly becomes moistened. Wedges of wood are sometimes 
driven into stones and then moistened: the capillary force 
splits the stones. Heavy weights are sometimes raised by 
wetting the ropes sustaining them. Blotting paper acts 
by the capillary force of its pores. Insects can walk upon 
water because their feet repel the water. An oiled needle 
will float upon water for the same reason. Sap fills the 
pores of plants because they are capillary tubes t 



Fig. 12. 

Two balls that act upon a liquid 
similarly, Fig. 12, quickly float to- 
gether: while if one attracts and the 
other repels the water, they will sepa- 

74. Osmose. If two liquids of 
different density be separated by 
a thin porous membrane, the 
outer liquid begins to pass inward, 
and the other outward. The for- 
mer is Endosmose; the latter, 

75. The phenomena of Osmose 
are best shown by the Endosmom- 
eter, Fig. 13. This consists of a 
bladder tied firmly to a glass tube, 
and filled with some liquid, as a 
strong solution of sugar, or pure 
alcohol. The whole is then im- 
mersed in water, the point where 
the liquid stands in the tube 
marked, and the apparatus left for 
sometime. The liquid soon rises in 
the tube, while sugar, or alcohol is 
found in the liquid outside. This 
shows that a current has passed in 
each direction, but the endosmose 
has been the greater. 

76. The currents are gov- 
erned by the following laws: 

I. The liquids must be capa- 
ble of mixiny. 

Fig. 13. 

II. They must be of different densities. 

III. The membrane must have yreater adhesion for one 
than for the other, and the former passes the more rapidly. 


77. Osmose of Gases is readily shown by 
placing a jar of hydrogen with a bladder 
tied over one end, Fig. 14, under a bell jar 
of carbonic anhydride. The hydrogen pass- 
es so much more rapidly than the carbonic 
Fig. 14. anhydride as to distend the bladder. If the 

hydrogen be inside the bladder, it is drawn inward. 

78. Osmose is of the greatest importance to animal life, 
since by it the food passes through the membranes of the 
intestines, the blood supplies nutriment and removes dead 
matter; and most of the functions of the organs are car- 
ried on through its action. Osmose of gases also takes 
place in the lungs. 


1. Section 47. A wire 2 metres long is lengthened 2 
millimetres by a load of 10 kilogrammes. What would be 
its length when stretched by a load of 15 kilos ? 

2. Two steel wires of the same length, whose diameters 
are respectively ^ and -rV inch, are stretched by the same 
weight: the former is elongated -rV inch: what is the elon- 
gation of the latter? 

3. The smaller wire of problem 2 sustains 1000 pounds. 
What weight applied to the larger would stretch the wires 
equally ? 

4. Section 48. When the sustaining wire is 1 metre long, 
a force of 2 kilos turns the index 10°. How many degrees 
would 7 kilos turn it ? 

5. Determine the length of the wire of problem 4 when 
the second force turns the index 30°. 

6. Section 57. Compare the friction upon the axles of a 
R. R. car when carrying a load of 10 tons, with the same 
car loaded with 30 tons. 

7. Compare the friction of an ice boat moving 10 mile^ 


per hour, with the same boat sailing 64 miles per hour. 
Section II. Gravitation. 

79. All the material particles in the universe attract 
each other. The force which causes this is called Universal 
Attraction, or Gravitation. The action is mutual, and be- 
cause of it, all bodies tend to approach each other. Were 
it not counterbalanced by other forces, all bodies would 
unite into a single mass. 

80. Though the existence of such a force was previously 
suspected, Sir Isaac Newton first demonstrated its existence 
and unfolded its laws. 

They are I. The attraction between bodies is proportional 
to the product of their masses, 

II. The attraction is inversely proportional to the square 
of the distance between the bodies* 

81. Since Newton's time, these laws have been proved 
experimentally by means of a delicate torsion balance,f 
which showed the attraction between a large ball of lead 
and a small one of copper. This experiment has also been 
used to measure the attraction of the earth. 

82. The spherical shape of large bodies like the planets, 
results from Gravitation, and its laws also govern their 
motions. Terrestrial Gravitation, with its result, the fall 
of bodies, is a special case. 

83. Plumb Line. The direction in which a body falls, 
that is the direction in which gravity acts, is a vertical line, 
and the line prolonged to the heavens marks the Zenith. 
It is usually determined by the plumb line, which consists 
of a ball of lead, called the bob, suspended by a string and 

*This second law, known as the law of inverse squares, applies to all radiant 
+See Section 99. 



Fig. 15. 

allowed to come to rest. Such 
a line points to the centre of 
the earth. 

For this reason plumb lines at 
different points as V and V" are 
not parallel, while they may even 
be at right angles to each other, as 
the horizontal and perpendicular 
plumb lines of Fig. 15. 

84. A plane perpendicular 
to the vertical is called hori- 

ig. ic. 


A liquid at rest, Fig. 16, presents a horizontal 

85. Deviation of the Plumb line. A 

plumb line suspended near a large mass of 
matter, e. g., beside a mountain, is attracted 
by the mountain as well as by the rest of the 
earth. This causes it to move towards the 
mountain, and the angle which it makes 
with the vertical is the deviation of the plumb 

Dr. Maskelyne 
suspended a plumb 
line upon opposite 
sides of Mt. Sche- 
hallien, in Scot- 
land, see Fig. 17, 
and found the de- 
viation of each to 
be about six sec- 
onds of arc. From 
Fig. 17. this he determined 

the attraction of the mountain, and then the density of the earth. 

He found the last to be about five times the density of water. 

86. Centre of Gravity. Since the earth attracts each 



separate molecule of a body, each body must have a point 
around which all the molecules will be arranged uniformly. 
Considering gravity as a system of parallel forces,* it is 
the point of application of the resultant. Suspend a body 
by this point, and it will remain at rest in any position. 



Determination of the Centre of Gravity. If a material line 
well represented by a wire, be balanced upon 
the edge of a knife, it will remain horizontal 
when the knife is at the centre. So too, if 
balls of equal weight be attached to the 
ends. But if the balls be of unequal weight, 
Fig. 18, then it will balance when the knife 
Hence the centre of gravity of a line is at 

Fig. 18. 
is nearer the larger, 
the middle point. 

88. If a triangle, Fig. 19, be suspended by one angle and 
a plumb line allowed to hang beside it, the plumb line 
passes through the centre of gravity. Kepeating this 
with a second angle, the centre of gravity will be at the 
intersection of the lines. This point is one-third the 
distance from the side to the opposite angle. 

89. Similarly by suspension and the plumb line, the 
Fig. 19. centre of gravity of a square, or a parallelogram is at 

the intersection of the diagonals. The centre of gravity of a cir- 
cle is at the centre. 

90. So the centre of gravity of any ir- 
regular body, as a norse and ball, Fig. 
20, may be found by suspending it by 
any three points, and the intersection 
of the lines indicated by the plumb 
line will be the centre of gravity. 

91. The centre of gravity 
may coincide with the cen- 
tre of mass, as in a truck 
made of uniform materials; 
or may be at one side, as 
when one side of the truck 
is loaded with lead; or may 

*See Section 134. 



even be entirely without the mass, as in the case of a ring. 

92. Line of Direction. A line joining the centre of 
gravity of the earth and the centre of gravity of any body 
is called the Line of Direction. The stability of bodies 
depends upon its position. To render a body as stable 
as possible, the line of direction should pass through 
the centre of the base, and the stability is increased by 
bringing the centre of gravity as near the base as possible. 

93. A body will fall when the line of direction falls 
without its base, because the centre of gravity is not sup- 

Thus the tower, Fig. 21, will stand when 
perpendicular, because the line of direc- 
tion then falls within its base. But when 
inclined, it falls, for the line of direction 
is then without. But if a portion of the 
top be removed, it will stand, for the 
centre of gravity is now lowered, so that 
the line of direction falls within the base. 

94. Applications. A load of hay is 
more easily overturned than a load 
of stones, because the centre of 
gravity being higher, the line of 
direction is sooner thrown with- 
A man leans forward when going up hill, 

Fig. 21. 

out the base. 

and backward when descending, to bring the line of direc- 
tion within the base. So with a load upon his back, he 
leans forward. Upon this principle, the leaning tower of 
Piza stands firm. Vessels and cars ought to be loaded with 
the heavy articles at the bottom to render them stable. 

95. Equilibrium. When all the forces which act upon 
a body neutralize each other, the body remains at rest. It 
is then said to be in Equilibrium. Tt presents three cases, 
Indifferent, Stable, and Unstable Equilibrium. 



Indifferent Equilibrium. When a body is sup- 
ported by its centre of gravity. In this case 
the application of any external force will 
only cause the body to move around its point 
of support and assume a new position. 

A truck supported by its centre, or if loaded on 
one side, near that side, Fig. 22, is a good illustra- 
tion. So a sphere of iron floating in a vessel of 
Fig. 22. mercury is in indifferent equilibrium. 

97. II. Stable Equilibrium results from supporting a 
body by a point directly over its centre of gravity, as the 
truck by the point b, Fig. 23. In a 
similar way, a body supported so that 
the line of direction falls at the middle 
of its base is in stable equilibrium. 
Any external force then raises the cen- 
tre of gravity, and after a few back 
and forth movements carrying the cen- 
tre of gravity through m and n, it assumes its former po- 
sition. A truck with a mass of lead near one side, but 
supported by the centre of volume is a good illustration. 

98. in. Unstable Equilibrium is presented by a body 
suspended directly beneath the centre of gravity, as the 
truck of Fig. 23 by the point c. Any external force tends 
to cause the centre of gravity to descend through an arc, 
and the body assumes the position of stable equilibrium. 
A sphere loaded at the top and placed upon a table is a 
good illustration. 

99. The Balance is an instrument for determining the 
amount of matter a body contains compared with the 
standard. In this way, weight is the measure of the earth's 



Fig. 24. 

attraction upon the body. Hence the absolute 
weight of a body must vary with its distance from 
the centre of gravity of the earth. The weight is 
then zero at the earth's centre, because the earth 
attracts equally in all directions, and most at the 
surface, while above, it diminishes inversely as the 
square of the distance from the earth's centre of 
gravity. For the same reason, a body weighs more 
at the level of the sea than upon a mountain, and 
more at the poles than at the equator. But the 
ordinary balance will not reveal this difference, 
since the weight and the standard are both affected 
equally. The spring balance, Fig. 24, shows the 
condition clearly. 

100. The ordinary Balance, Fig. 25, is a lever of the first class* 
with the two arms equal. To secure lightness and strength, the 
beam is usually made as a frame, and is supported by a knife 
edge of polished steel resting upon a plate of agate, so as to 
turn with very little friction. Scale pans similarly supported 

Fig. 25. 

are placed at the ends, and there is an index at the centre to 

*See Mechanics, Section 157. 




enable the observer to see slight variations. It is placed in stable 
equilibrium by bringing the centre of gravity a little below the 
knife edges, and wear is prevented by lifting the beam free from 
the bearings when not in use. 

101. A good balance should meet th e following conditions : 

I. The two arms should be precisely equal, or unequal 
weights will produce equilibrium. 

II. The beam must be in equilibrium with empty pans. 

III. When the beam is horizontal, the centre of gravity 
and the point of support must be in the same vertical line. 

Correct results can be obtained from an inaccurate bal- 
ance, provided it is sufficiently sensitive, by the method of 
double weighing. The body to be weighed is put into one 
scale pan, and sufficient shot or sand poured into the other 
to bring the balance into equilibrium. The body is then 
removed and sufficient weights placed in the 
empty pan until the equilibrium is again ob- 
tained: their sum is the weight of the body. 

102. Laws of Falling Bodies. The attrac- 
tion of the earth acts equally upon all the 
molecules of which a body is composed. 
Hence all bodies ought to fall with equal 
rapidity, regardless of their volume or density. 
That they do not, must then result from the 
resistance of the air. 

This is proved experimentally by the Guinea 
and Feather Tube, Fig. 26. This is a glass tube 
about two metres long, closed with a brass cap at 
one end, and a stop-cock at the other, by which it 
can be connected with an air pump.* When filled 
with air, a coin and feather within fall at different 
Fig. 26. rates: after exhaustion, both fall together. 

*See Section 300. 



103. Attwood's Machine. Bodies 
fall so rapidly that the time required 
for their fall cannot be readily deter- 
mined. Attwood's Machine is em- 
ployed so to reduce the rate of falling 
as to render it measureable, Fig. 27. 
It consists of a wooden pillar about 
eight feet long divided into feet and 
inches, with a large wheel at the top 
moving with very little friction. A 
silk cord passes over this, and equal 
weights are attached to its ends, so 
placing them in equilibrium. A 
hinged platform is placed at the top, 
held in place by a lever which is 
moved by the armature of an electro 
magnet. A pendulum beating sec- 
onds is placed so as to form a part of 
the electrical circuit, and this carries 
a small point which passes through 
a drop of mercury placed upon a 
small iron shelf on the wooden column. 
When the pendulum passes the mer- 
cury, the current is completed, the 
platform falls, a bell rings, and con- 
tinues to ring each time the pendulum 
passes the mercury, thus showing the 

104. 1st Experiment. Place a 

small additional weight, called the 
over weight,* upon the weight 
which rests upon the hinged plat- 
form, and allow the pendulum to 
beat. The weight falls, and at 
the end of one second has reached 
one foot ; at the end of two seconds, 
j^^T^ four feet ; at the end of three sec- 

onds, nine feet, and so on. Hence the First Law. The spaces 
passed over by a body vary as the square of the times of falling. 

*A convenient overweight is one-sixteenth the sum of the weights. 


105. The distances passed in each second are found by 
subtracting the distance already passed, and vary as the 
odd numbers. 

106. If the overweight is -^ of the sum of the two 

weights, the distance represented by one foot, or one space, 
is sixteen times the space passed, or sixteen feet, or more 
exactly, 16^ feet. 

107. 2d Experiment. To determine the velocity or 
rate at which the body moves. At the beginning of the 
first second, the body is at rest and its velocity is zero. 
Attach a ring platform to the pillar, just large enough to 
allow the large weight to pass through, but not the over- 
weight, and place this one foot from the top. Cause the 
pendulum to beat, and at the end of the first second the 
overweight will be removed. Since the weights are now 
equal, they are no longer acted upon by gravity, but move 
forward by their inertia at the rate they were moving 
when the overweight was removed, which is the velocity 
already acquired. At the end of the second second, the 
weight is three feet from the top, that is, has moved two 
feet during that second. So the velocity at the beginning 
of that second was two spaces. Hence the Second Law of 
Velocity. The velocity acquired in falling any distance 
will carry the body twice that distance in the next equal 
space of time. 

108. These Laws give the following Table, in which 
16 T V feet equal one space : 


Distance fallen 
in each. 


Total Distance. 
1 * .. 

Velocity at 



: 3 



3. .... 



. 4 















109. The Pendulum. If a heavy weight is suspended 
by a string, it vibrates back and forth. This arrangement 
is termed the Compound Pendulum. A single molecule 
suspended by a material line and allowed to vibrate is a 
Simple Pendulum. Since the molecules of a compound 
pendulum are at different distances from the point of sup- 
port, they tend to oscillate at different rates. There is 
one point which tends to move at the rate of the pendulum 
and this is called the Centre of Oscillation. Hence, the 
length of a Compound Pendulum is the length of a Simple 
Pendulum which will oscillate in the same time. 



Fig. 28. 

110. Laws of the Pendulum. To determine 
the laws experimentally, the apparatus of Fig. 
28 is used. It consists of several pendulums 
attached to a frame. One of them is moved a 
little distance and allowed to oscillate Gravity 
carries the pendulum to the lowest point, C, 
Fig. 29. Inertia, or the 
acquired velocity, car- 
ries it in opposition to 
gravity until one equals 
the other, or to the 
point D. Then the pen- 
dulum stops and repeats 
the operation. The time 
of the oscillation is not- 
ed. Increasing the arc 
does not vary the time. 

Fig. 29. 

Law I. While the arcs remain small, the time of oscilla- 
tion remains constant. 

111. Trying pendulums of the same length but of different 
materials, e. g. wood and lead, Fig. 28, they vibrate together. 

Law II. The time of oscillation is independent of the 
substance used for the weight. 


112. Causing a pendulum to vibrate with one of four times 
its length, the short one is found to make two vibrations to one 
of the other. Hence 

Law III. The time of oscillation varies inversely with 
the square root of the length of the Pendulum. 

113. Application of the Pendulum to Clocks. A clock 
is merely a train of wheels moved By a weight or spring, 
with an attached index to record the number of beats of a 
pendulum. The wheels move an escapement wheel. A 
fixed piece called the escapement or crutch, terminating in 
projections or pallets, catches the teeth of the wheel with 
the pallets alternately, so allowing one tooth to pass at 
each beat of the pendulum. At the same time, a fork sur- 
rounding the pendulum rod strikes a slight blow upon it, 
just sufficient to overcome the resistance of the air, and 
this keeps the motion continuous. 


1. Section 80. The mass of the earth is 1 : that of the 
moon .0123. How much more does the earth attract the 
moon than the moon the earth? 

2. What will a kilogramme weigh 4000 miles above the 
earth's surface? 

3. What will a kilo, weigh at the centre of the earth ? 

4. Section 83. What angle will two plumb lines make 
with each other, if placed 1000 miles apart ? 

5. Section 108. Determine the velocity acquired by a 
body in falling to the surface of the earth from a balloon 
one mile high? 

6. How long will the body of problem 5 be in falling? 

7. A rifle ball leaves the surface of the earth perpen- 


dicularly with a velocity of 80 ft. How high will it rise ? 

8. How far will it go ? 

9. How long will it remain in the air? 

10. Section" 112. A pendulum vibrates once in five sec- 
onds. How many metres long is it ? 

N. P. 3. 


114. An External Force acts upon a body as a whole, 
in place of acting upon its molecules, as do those forces 
considered previously. External forces are of two kinds, 
Impulsive and Undulatory. 



115. Impulsive Forces act for a moment only. This 
separates them distinctly from attraction, which always 
acts, and hence is called a constant force. 

116. An impulsive force may produce its effect upon 
a bod} r where it is applied, or it may move through the 
body in virtue of its elasticity and affect some other body 
situated beyond that to which it is immediately applied. 

117. Representation of a Force. Forces are conven- 
iently represented by straight lines. The origin of a line 
indicates the point of application of the force ; its direc- 
tion, the direction in which the force acts ; and its length, 
the intensity of the force ; and it may be drawn upon any 
given scale. 


118. Unit of Force. The unit of force is the force 
required to move one kilogramme one metre in one sec- 
ond. It is called a kilogramme-metre.* 

119. Action and Reaction. When an external force acts 
upon a body, the body opposes the force applied. The 
efiect of the force is action, and the opposition of the body, 
reaction. Thus a book placed upon the table presses upon 
it by an amount equal to its weight. But the table presses 
upward an equal amount and prevents it from falling. Or 
if two persons pull equally upon opposite ends of a rope, 
the rope is not moved. Now if one person be replaced by 
a hook firmly fastened to the wall, the effect upon the rope 
is not changed. 

120. Law. The relation of action and reaction is then 
expressed by the following law: Action and Reaction are 
equal, hut in opposite directions. 

Section I. — Movements of Forces. 

121. Forces which produce their effects by the aid of an 
intervening body may travel in two ways, by a movement 
of the molecules of the body, or by a movement of the entire 
mass of the body at once. Both acts are called transmis- 
sion of force. 

122. Inelastic bodies when struck, yield to the blow. If 
such bodies transmit force, both bodies move forward to- 
gether after impact, and the velocity is reduced to that 
resulting from their combined momentum. Such trans- 
mission is not applied practically. 

123. Transmission of force by movements of the mole- 
cules in elastic bodies consists in pushing the molecules to 
one side, or in changing their relative position. But the 

*If the English system is used, the unit of force is the force that will move 
one pound one foot in one second, and it is called the foot-pound. 



elasticity of the body instantly returns them to their 
original position, after producing a similar movement of 
the next series of molecules, and so on. The final mole- 
cules give the force to the succeeding body. 

124. The movement of force by molecules 
is well illustrated by the collision balls, Fig. 
30. If the first be drawn out and allowed 
to fall upon the next, the force is transmitted 
undiminished, except by a lack of elasticity, 
to the last, which moves out as far as the 
first was drawn out. So if a long pine rod 
be firmly fastened to a table, either by a 
small vise or by pressing upon it, and a ball 
be placed at one end, a smart blow upon the 
other end will drive away the ball. 

125. When a force is transmitted by 
Fig. 30. a movement of the intervening body 

as one mass, the velocity is diminished by the resistance 
due to the weight of the intervening body. This is well 
illustrated by allowing the rod and ball of the preceding 
paragraph to rest freely upon the table, and again striking 
the rod. Now both move. 

126. This last method has a practical application in the 
piston rod of the steam engine, as it transmits the force to 
the walking Jbeam, or to the crank. 

Section II. — Composition and Resolution of Forces. 

127. Frequently one force is required to do the work 
previously done by several. Finding such a force is Com- 
position of Forces, and the force is a Resultant. On the 
other hand, it is sometimes necessary to separate one force 
into several. The process is Resolution of Forces. Both 
processes can be treated together, since one is the reverse 
of the other. 



Fig. 31. 

128. First. When several Forces act along a line, the 

resultant is the algebraic siim of the forces. 

Thus if A, B, and C, Fig. 31, 
act upon the material point X in 
the same direction, the resultant 
will be the sum of these forces. 
But if one of them, as B, Fig. 

PBL W RRI ^' acts in tlie °P posite clirec- 

I tion, the resultant is diminished 
^^"^^^^^^^^^^^^^^^^™ by that force. So in an oppo- 
g * 32 " site way, a single force can bo 

separated into any number of parts acting along the same line. . 

129. Second. Parallelogram of Forces. Each force that 
acts upon a body must produce its effect, whether acting 
alone, or with other forces. So a body acted upon by two 
forces at an angle must move in two directions at the same 
time, and must travel as far in each direction as though it 
were moving in no other. 

Thus the force B, Fig. 33, acting 
upon the body A with an intensity 
of A B, will move the body in the 
direction A B as far as B in the 
unit of time. So also the force C 
must move A as far as C in the di- 
rection AC in the same time. Hence 
the body A will be found at D, the 
only point which meets the two 

Fig. 33. 

conditions, while to reach that 
point it will travel along the diagonal of the parallelogram. 

Hence to find the resultant of any two forces acting at 
an angle, complete the parallelogram of which the two 
forces make the two sides, and draw the diagonal from the 
point of application of the forces. Its direction will be 
the direction of the resultant, and its length, the intensity. 

130. So a single force may be resolved into two compo- 
nents acting at any given angle with each other, provided 


the angle which one makes with the original force is given. 
In this case, the given force will be the diagonal A D of a 
parallelogram, of which the new forces, A B and A C, make 
the sides, and their intensity will be determined by com- 
pleting the parallelogram. 

131. When there are several forces acting upon a point 
in the same plane, the resultant of all is obtained by find- 
ing the resultant of any two, then using this resultant as 
a new force, and finding the resultant of that and a third 
force, and so on until all are used. The final resultant is 
the resultant required. 

Thus let A, C, D, E, Fig. 34, be four 
forces acting upon the body B. Draw 
the parallelogram B A F C and B F is 
the resultant. Then using B F as one 
side and B D as another, complete the 
parallelogram B F G D, and B G is 
the resultant. So with the parallelo- 
gram B G H E and B H is the resultant 
of the four forces. 

132, Since one resultant can be 
found to replace all forces acting 
on a point, and this resultant can 
be resolved into forces acting at a 
Fig. 34. given angle, any number of forces 

in the same plane, acting upon a point in different directions, 
produce the same effect as two forces acting at right angles 
to each other. For such forces may be first compounded 
to obtain a resultant, and then the resultant may be resolved 
into two components at right angles to each other. This 
principle finds practical application in polarization of light.* 

133. Third. Parallelopiped of Forces. The resultant 
of three forces acting upon a body, but in different planes, 
is found by making the forces three edges of a parallelo- 

*See Optics, Section 636. 



piped, completing the solid, and drawing its diagonal from 
the body. The diagonal represents the resultant both in 
direction and intensity. 

134. Fourth. Parallel Forces. 

Parallel Forces are applied at dif- 
ferent points of a body, but in the 
same direction. 

Thus A C and B D, Fig. 35, are two 
equal forces acting upon an inflexible 
bar A B. Their resultant, E F, is the 
sum of the two, since both act in the 
same direction. It is evidently applied 
to the middle point, as they are equal. 

Flg ' 35, 135. If one force is greater 

than the other, the resultant will be nearer the greater. 

Hence the distance of the result- 
ant will be inversely as the forces. 
That is, Figure 36, B D:A C= 

136. The resultant of several 
forces may be found from the re- 
sultant of two combined with a 
Fig. 36. thirdi and so on T}lis ig iUug _ 

trated in the case of Gravity.* Considering a body as 
made up of molecules each of 
which is acted upon by gravity, 
the line of direction becomes the 


137. The principle of parallel forces 
admits of experimental proof by means 
of the apparatus cf Fig. 37. Two 
weights are suspended by a bar, and 
Fi »- 37 - the distance from the point of sup- 

port is inversely as their mass. 

*8ee Book I, Section 



138. If iwo forces 1 act in opposite directions, the result- 
ant is their difference. 

Thus in Fig. 38, B D acts in a direc- 
tion opposite to A C. E F, the result- 
ant, is their difference. But it must 
be applied beyond A at E. so that the 
distance shall be inversely propor- 
tional, as before ; that is BD:AC= 
AE:EB. • 

Fig - 38 - 139. A Couple. Two equal op- 

posite parallel forces have no resultant. 

Thus A C and B D are two equal and 
opposite parallel forces. Obviously 
the entire effect of such an arrange- 
ment is to produce revolution. No 
one force can replace them. Fig. 39. 

140. In all cases, if a force 
equal to the resultant be applied 
in the opposite direction, it will place the system in equi- 
librium and cause all motion to cease. 

Fis. 39. 



141. An oidulatory force produces vibrations in an 
elastic medium. These vibrations are transmitted to an 
indefinite distance, by a change of position, or of shape of 
the molecules of the medium. When the vibrations are 
transferred from the medium to the human body, they give 
rise to their appropriate sensations. 

*If thought best this Chapter can be omitted until the completion of Book m. 


142. The movements of the molecules of the medium 
may be longitudinal or transverse. 

143. Longitudinal Yibrations are movements of the 
molecules in the direction in which the force is moving. 
When such vibrations reach the ear, if of proper length 
and intensity, they give rise to the sensation of sound.* 

144. Transverse Yibrations are movements of the mol- 
ecules of a body at right angles to the direction in which 
the force is moving. When such movements are arrested 
by any body, the force is expended in producing a perma- 
nent increase in the movements of its own molecules, that 
is a rise of temperature. Reaching the nerves of the body, 
such vibrations give rise to the sensations of heat and light.f 

145. The force called Electricity also travels by a move- 
ment of the molecules of the conducting body, but whether 
by a longitudinal, transverse, or mixed movement is not 
known. The fact of movement is proved by the weakness of 
a conducting wire after long use, growing out of a rear- 
rangement of its molecules, that is a crystallization. 

146. Waves in Liquids. When the surface of a liquid, 
as a lake or pond of water, is disturbed by an external 
force, as dropping a stone into it, the disturbance gives rise 
to a series of waves that enlarge from that point as a centre 
indefinitely. A single wave carefully followed by the 
eye, is seen to move forward unaffected by its neighbors. 
The length of Fig. 41 represents the length of the wave, 
and the diameter of the circles, its height. The part raised 
above the surface of the water when at rest, is the crest; 
that below the surface, is the trough. 

147. Movements of the Molecules. The molecules of 

♦See Acoustics, Book IV, Part I. 

+See Heat and Light, Book IV, Parts II and III. 



the liquid have a vertical motion, or up and down ; and 
also a rotation upon an axis. The vertical movement is 

well illustrated by Snell's Ap- 
paratus, Fig. 40.* A series of 
keys is moved by an eccentric 
so that as the crank is turned, 
they move up and down. Fol- 
lowing their toj>s with the eye, 
the vertical movement of the keys causes a forward move- 
ment of the wave. 

148. The 

revolution of 
the molecules 
themselves is 
shown by Ly- 
man's Appa- 
ratus, Figure 
41. This con- 
sists of two se- 
ries of revolv- 
ing cranks at- 

Fig. 41. 

tached to wires. As the wire which represents the wave 
is moved, the cranks which represents molecules revolve. 
Hence waves have both movements of the molecules. 

*The pieces of apparatus represented by Figs. 10 and 41 are made by Mr. E. 
S. Ritchie, of Boston, Mass, 



149. Mechanics treats of the effects produced upon 
bodies by external forces. Since bodies may be in either 
of the three states, there are three general divisions of the 
subject, Mechanics of Solids, Mechanics of Liquids, and 
Mechanics of Gases. 



150. Since, in a solid, attraction exceeds repulsion, the 
body maintains its general shape ; and the effect of an 
external force acting upon it as a whole is change of po- 
sition. This change may be effected by applying the force 
directly to the body, or by the aid of some intervening 
body or series of bodies called a machine. So any change 
may continue until a body yields to the force applied and 
breaks; and the point where the fracture occurs depends 
upon the strength. Hence Mechanics of Solids has two 
general divisions, the Simple Machines, including their 
combinations, and the Strength of Materials. 



Section I. — The Simple Machltos. 

151. The Simple Machines are the Cord, the Lever, and 
the Inclined Plane. The others sometimes given are com- 
binations of these. All machines, however complex, are 
applications of these powers. 

152. The Cord, theoretically, is an inelastic flexible line, 
without weight, used to change the point of application of 
a force. Practically, the cord is somewhat elastic, not per- 
fectly flexible, and has weight. Thus a rope used to move 
a weight at one end, with the power applied at the other, 
is a cord. The cord is used in combination with the lever, 
in the pulley, the wheel and axle, and in belts. 

153. The Lever, theoretically, is an inflexible bar, with- 
out weight, turning freely upon a support called the 
fulcrum, with the power applied at one point, and the work 
done at another. Practically, the lever has some weight 
which must be considered in the calculation. 

0~ '' /~\ST7m Tnils tne bar > Fi &- 42 > is a lever: tlie 
_^' h^ block is the fulcrum, the small weight is 

jp IjlP the power, and the large one the weight 

~ " = *" to be raised. They are in equilibrium. 

154. Equation of the Lever. Let L be the distance of 
the power from the fulcrum, and S the distance from the 
fulcrum to the weight: then PL=WS. From this, either 
term can be obtained when the others are known. This 
equation applies to all levers. 

155. Classes of the Lever. There are three classes of 
the lever, depending upon the relative position of the power, 
weight and fulcrum. 

156. The Lever of the First Class has the fulcrum be- 
tween the power and the weight. Thus the lever of Fig. 



42 is of the first class. If the arms are equal and motion 
is given, power and weight will move equal distances. If 
the power arm is longer than the other, the power will 
move further than the weight. 

157. Applications of this lever are numerous. A bar 
used to pry out a stone, or to draw a spike, a pair of scis- 
sors, and the balance* may be mentioned. 

158. The Lever of the Second Class has the fulcrum at 
one end, and the weight between that and the power, Fig. 

43. In this case, the part of the 
bar between the fulcrum and the 
weight is employed in both long 
and short arms, and the power 
and the weight move in the same 

159. Applications. 

Fig. ii. 

A man raising a stone, Fig. 44, uses 
a lever of the second class. The 
wheelbarrow has the fulcrum at the 
wheel, the load in the barrow for the 
weight, and the hands for the power. 
Nutcrackers, lemon-squeezers, and 
similar articles, and a door swung on 
its hinges by the knob are also levers of this class. 

160. The Leyer of the Third Class has the power be- 
tween the fulcrum and the 
weight. Thus W F, Fig. 45, 
is a lever of the third class. 
The weight is less than the 
power, but moves more rapidly. 

161. Applications. Sugar tongs are levers cf this class. 
A man raising a ladder against a building is the power; the 

^See Section 100. 



ladder is the weight, applied at its centre of gravity, and the 
building is the fulcrum of a lever of the third class. The 
principal muscles of the body act as levers of this class. 
Thus a weight raised by the hand is lifted by the muscles 
attached at the elbow. The muscle acts at a great me- 
chanical disadvantage, but it is compensated for by the 
more rapid movement of the hand. 

162. A lever may be bent as well as straight; and the 
power and the weight may act at any angle. In either 
case, the true length of the arm is the length of a perpen- 
dicular from the fulcrum to the direc- 
tion in which the force acts. Thus 
N F, Fig. 46, is the long arm, and M F 
the short arm of the bent lever A B, 
to which the power P is applied in the 

Fig. 46. direction B P, and the weight W in the 

direction A W. 

163. The Compound Lever, Fig. 47, consists of several 
simple levers so arranged that the 

1& power of the first is the weight of 
id the second, and so on. It is ap- 
plied only when great weights are 
to be moved a short distance. The 
powerful scales used for weighing 
Fi e- 47 - hay and coal are arrangements of 

compound levers. 

164. The Pulley is a cord bent around a support, so 
changing its direction. A wheel with equal 
arms, which is a lever, is usually used to di- 
minish friction. Thus the cord P W, Fig. 48, 
passes over the top of the wheel and rests in a 
groove, while the parts of the wheel A F and 

Fig. 48. Y B are equal. Pulleys are of two kinds, 
Fixed and Movable. 



165. A Fixed Pulley, at the top, Fig. 49, is used simply 
to chrnge the direction in which a force acts. It enables 

the weight to rise with a downward movement of 
power. It is applied for raising weights to a height. 

166. The Movable Pulley, middle, Fig. 49, uses two cords 
to sustain the weight. By its use, the power then is doubled 
but the weight moves only half the distance traversed by 
the power. It is* commonly used in combination with a 
fixed pulley for raising heavy weights. 

167. The Tackle, near the right, Fig. 49, consists of sev- 
eral fixed and movable pulleys with a single rope wrapped 
around them all. For convenience, those at each end are 
usually placed side by side in a single block. The power 
gained is determined by the number of strands of rope, for 
each sustains its proportionate part. 

168. Pulleys with Different Ropes. Pulleys may also be 
combined, as at the left of Fig. 49, the rope which sustains 


one pulley being the weight of a second, and so on. In this 
case, the first rope sustains one-half the weight, and the 
second one-half of that, and so on. Hence in this case, 
the proportion is found by raising one-half to the power 
indicated by the number of cords or blocks. 

169. The Wheel and Axle, Fig. 50, is also 
a combination of the cord and a lever of the 
first class. By passing a cord around the 
circumference of a wheel and a second in the 
opposite direction around a second wheel of 
Fig. 50. less diameter called an axle, the action be- 
comes continuous. The radius of the wheel, AB, is the 
long arm, and the radius of the axle, CB, is the short 
arm of a lever of the first class. 

The wheel and axle is used in raising heavy weights, as 
is shown in Fig. 49. Frequently a crank replaces the 
wheel, and the hand describes a circumference correspond- 
ing to the circumference of the wheel, and then the 
arrangement is called a windlass. In this form it is fre- 
quently used for drawing water. 

170. The Capstan, Fig. 49, at the bottom, is simply a 
wheel and axle placed vertically. The bars, which are 
frequently made so as to be removed at pleasure, enable 
the operator to walk around it, so employing his strength 
to the greatest advantage. The sweep, often used in 
moving buildings, is another form of the same machine. 

L o^-i 

171. The crane is a combination of the windlass and 
a tackle. The derrick consists of a windlass and two 
tackles, one of which moves the weight and the other the 
arm which holds the weight. 

172. Wheel Work. Most arrangements of wheel work 
are combinations of the wheel and axle. Thus, in Fig. 51, 



Jl » ^ r & 

Fig. 51. 

the cogs on the rim of one wheel work into the cogs on 
the axle of the next, called a pinion. As each cog of the 
wheel moves one of the pinion, to determine the propor- 
tionate rate of revolution, divide the number of cogs on 
the circumference of the wheel by the number on the 
pinion. In raising a weight, as in the figure, such a train 
of wheels becomes a compound lever. The figure also 
shows the crank applied to move a heavy balance wheel. 

173. Wheels are frequently combined in this way to 
increase the rate of revolution, or as technically named, 
" to speed up, 1 ' by exchanging power for time. Such an 
arrangement is seen in the watch, where four revolutions 
of the main driving wheel, to which the spring is at- 
tached, produce twelve revolutions of the pinion which 
carries the minute hand. 

174. Another way that wheels are connected is by 

belts. In this way, the separate wheels, usually called 
N.P. <l 


pulleys, can be many feet apart. The power is transmitted 
by the friction of the belt upon the surface of the wheel, 
but since this is not perfect, some power is lost by the 
slipping of the belt. The middle of the pulley is a little 
larger than the sides to prevent the belt from running off- 

175. When the driven wheel and its shaft is required 
to move faster than the one driving it, the diameter is less ; 
and the rate of the two wheels compares as their circum- 
ference: when a slower motion is wanted, the driven wheel 
is made larger, and they compare as before. 

176. Centrifugal and Centripetal Forces. The inertia 
of the molecules which make the circumference of a re- 
volving wheel, tends to carry them forward in a straight 

line, that is in a tangent, A E, Fig. 52, to its 
circumference. This is called the Centrifugal 
Force. It is opposed by the cohesion of the 
wheel, which may be considered a force tending 
to pull the separate molecules towards the cen- 
Fig. 52. j- re> Tkis is the Centripetal Force. 

177. The manner in which these forces act may be 
experimentally illustrated by rapidly whirling a string with 
a ball at the end. The string represents the centripetal 
force, as the hand is constantly pulling upon it, while the 
tendency of the ball to move further away represents the 
centrifugal force. 

178. The water flying from a rapidly moving grindstone, 
and the mud from a carriage wheel, are illustrations of a su- 
perior centrifugal force. So if a wheel be revolved too 
rapidly, the cohesion is overcome and the wheel breaks, 
sometimes doing great damage. This is the cause of the 
great danger incurred in grinding gun barrels at armories, 
for the large stones employed always run at a rate very near- 
ly sufficientto overcome the cohesion, and a slight increase 



Fig. 53. 

of speed causes them to break. 
The motion of the planets in their 
orbits is an instance of the exact 
balancing of centrifugal and cen- 
tripetal forces. 

1 79. The flattening of the earth 
at the poles has been caused by 
centrifugal force. Fig. 53 illus- 
trates the process. Rapid revolu- 
tion causes the brass ring to en- 
large equatorially, and in conse- 
quence, the polar axis is shortened. 

This is the case with the earth. 

180. The Inclined Plane, Fig. 
54, is the third mechanical power. 
It consists of a plane placed at an 
angle to the direction in which 
the body is moved. It adds to the 
efficiency of a force by sustaining part of the weight. 

Fig. 54. 

181, The force which moves a body up an inclined plane 
may act parallel to the plane; paral- 
lel to its base; or at an angle between 
them. The last by the principle of 
resolution of forces, may be resolved 
into the first two. 

Fig. 55. 

182. First, when the force acts 
parallel to the plane, Fig. 55, the 
load W presses upon the plane in consequence of its weight. 
This acts perpendicular to the earth, and is the force ba. 
But ab, which is the resistance of the plane and the power, 
is made up of the components ac, the power, and ad the 
resistance of the plane. Hence ac:ab=P:W. But the 
triangles abc, abd and RST are all similar. Hence ac:ab= 



ST:RS, or P:W=ST:RS. That is, the power is to the 
weight as the height of the plane is to its length. 

183. Second. When the force is ap- 
plied parallel to the base, Fig. 56, a 
part is expended in increased pressure 
upon the plane. Hence since the trian- 
gles are again similar, Ac: cb= ST: TR. 
Fig. 56. But Ac represents the power, and be the 

weight. Hence the power is to the weight as the height of 
the plane is to its base. 

184. In both cases, the power increases with the length 
of the plane. But at the same time the weight is raised 
more slowly. 

185. The inclined plane is used in raising heavy weights, 

as in loading a block of stone. 
Ascending a hill, Fig. 57, 
and going up a flight of stairs 
are applications of the in- 
clined plane, the steps of the 
stairs being merely places to 

Fig. 57. put the feet. 

186. The Wedge, Fig. 58, consists of two in- 
clined planes united by their bases. Hence power 
is gained by it in the same way as with the plane-. 

187. The wedge is applied in raising weights a 
very short distance, in splitting wood and stone, 

Fig. 58. an( j - n Q^gj. cases where great power is to be gained. 
Because of friction, it is most effective when moved by a 
blow. Nails driven into wood, piles driven into mud, chis- 
els, knives, axes, and all edged tools are inclined planes or 

188. The Screw, Fig. 59, is an inclined plane wound 


around a cylinder. This is easily seen by 
cutting a paper inclined plane, and wind- 
ing it around a cylinder. It requires a 
hollow cylinder called a nut, having 
(j threads cut to correspond to those of the 
screw in which it turns. The distance 
Fig. 59. between the threads is called the pitch of 

the screw. The power is usually applied by a lever, whereby 
it is greatly increased. 

The Screw is employed in presses because it will re- 
main fixed in any place. This is due to the great loss of 
power from friction, amounting sometimes to ninety per 
cent. It is also used in raising buildings. Wood screws 
form their own nuts as they advance. 

189. All machines expend a portion of the applied force 
in overcoming the friction of the various parts. Hence 
all the formulae previously given are calculated to produce 
equilibrium. When motion is required, a small amount of 
weight must be added ; ' and all bearings should be kept 
well lubricated, to diminish the friction as much as possible. 

On the other hand, efficiency is often due to friction, 
as in the case of walking. Unless the loss be at least 
one-half, the machine will not hold the weight in position, 
if left to itself, but requires to be fastened- This is illus- 
trated by comparing the effects produced by a screw with 
those of a pulley. 


1. Section" 156. A lever of the first class 3 metres in 
length carries a weight of 1 kilo. 5 decimeters from the 
fulcrum. What power will balance the weight ? 

2. If the power of problem 1 descends 3 metres, how 
far will the weight be raised? 


3. Where must the fulcrum he placed in a lever of the 
first class 10 feet long in order that a power of 8 lbs. may- 
balance a weight of 40 lbs. ? 

4. Section" 158. What weight can a lever of the second 
class 5 metres in length raise, if moved by a power of 7 
kilos., provided the weight is applied 1.5 metres from the 
fulcrum ? 

5. Place 400 lbs. upon a lever 10 feet long so that one 
end shall support one-third and the other the remainder of 
the weight. 

6. Section 160. If a man's forearm measures 1 ft. and 
the muscle is attached \ an inch from the joint, how much 
power must the muscle exert to lift a ball of 96 lbs. placed 
in the hand ? 

7. A ball of 2 kilos, at one end of a lever of the third 
class 8 metres long is balanced by a power of 8 kilos. 
Where is the power placed? 

8. Section 163. With two levers arranged as in F.'g. 47, 
the weight is 1 T, and each lever is 10 ft. long. What 
power balances the weight ? 

9. Section 166. Required the power which will raise 500 
kilos, with one movable pulley. 

10. Raise 5 T 3 feet with the tackle of Fig. 49. What 
power is required, and how far will it move? 

11. Section 182. What power will balance a weight of 
56 lbs. resting upon an inclined plane whose base is 1 ft. 
and height is 6 inches? 

Section II. — Steength of Matekials. 

190. The limit to the size of any machine, or structure, 
is the strength of the materials employed. When this 


limit is reached, additions to its mass add nothing to its 
strength, and if continually made, a point is ultimately 
reached at which the structure crumbles from its own 

The strength of a structure depends also upon its shape. 
Hence the subject includes two topics, the strength of 
different substances, including the shape in which they 
best resist strain ; and the principles involved in combining 
the parts into buildings and machines. 

191. First. Resistance to Strain. An applied force may 
produce rupture in either of three ways: it may act to 
crush the body, called crushing strain; or it may tend to 
pull the body apart in opposition to cohesion, longitudinal 
strain; or it may act at right angles to the length of the 
body, resisted both by cohesion and elasticity, transverse 

192. The weight of a structure resting upon the foun- 
dation is an illustration of the first case. Such a load 
diminishes the vertical thickness of the foundation, and if 
sufficiently increased, crushes it. If the materials were 
homogeneous, when the body gave way, it would crumble 
to a powder. Practically, it breaks in several places. 
Hence such materials must be selected for the foundation 
as are able to sustain the weight of the structure and re- 
move all risk of being crashed. The size is determined by 
crushing a small cube of the substance, and from the 
weight employed, determining by simple proportion the 
size necessary to sustain the structure. To insure safety, 
the foundation should be three times the size calculated. 

193. The second Method is illustrated by a rope sustain- 
ing a weight, or in a timber holding a load attached to its 
lower end. Since elasticity of traction commonly exceeds 
elasticity of pressure, this method of applying a stress is 



better than the first, and should be used wherever possible. 

194. The most common way of applying a load to a 
beam is by a transverse strain. The first result of such a 
stress is to bend the sustaining beam. Fig. 60. The mole- 
cules (represented by the 
circles) on the side to- 
wards the load L applied 
to the top, are pressed 
Fig. 60. nearer to each other, re- 

sisted by elasticity of pressure; while those on the other 
side are moved farther apart, opposed by elasticity of trac- 
tion. Three cases demand consideration. 

] 95. First, when a beam is fast- 
ened at one end, and the load is ap- 
plied at the other, Fig. 61. The 
fracture must take place at the point 
of support, beginning at the upper 
Fig. 6i. surface, at A. A beam so arranged 

will sustain the least load of any arrangement. Let this 
be W. 

196. Second. A similar beam, with the load at the same 
distance from the point of support, may rest freely upon 

two sustaining posts, Fig. 62. In 
this case, the load is distributed 
equally between two points of 
Fi #- 62 - support. Hence the amount re- 

quired to produce fracture is double that in the first case, 
or 2 W, and the fracture commences at the under surface. 

197, Third. The beam may be supported as in case 
second, but both ends be securely 
fastened. Fig. 63. In this case, 
fracture must occur at both ends, 
and in the middle at the same 
Fi s- 63 - time. But W is required to break 


each end, or 2 W to break both, and 2 W to fracture the 
middle. Hence such a beam will sustain 4 W. 

198. Practical Applications. All beams should be three 
times as large as necessary to sustain the load, to insure 
safety, and this multiplication by three is called the factor 
of safety. All beams should have the load as equally dis- 
tributed as possible, and should be firmly fastened at the 
ends. Where possible to avoid it, no beam should be used 
with one end unsupported. 

199. The most economical arrangement of materials is 
in the form of a hollow cylinder, for the size of the cyl- 
inder can not be changed without crushing all parts. This 
form is therefore employed in cast iron columns, which 
yield much less readily than solid columns of the same 
weight. The bones of animals, and the feathers of birds 
show the same arrangement. 

200. Beams, to offer the greatest resistance, should be 
as deep as possible in proportion to their thickness, since 
this places the greatest possible number of molecules in 
position to resist the movement which precedes fracture. 
This is illustrated by the ease with which a board is bent 
and broken when laid down, and the great weight it will 

sustain when placed on its edge. Hence the 
depth of all timbers should be several times 
their thickness. Experience has shown that 
iron beams are best made in the form of a 
double T., Fig. 64, with the height about twice 
Fig. 64. the thickness at the broadest part. 

201. Second. Principles of Frames. The combinations 
of materials into buildings and machines are all applica- 
tions of a few simple principles. The most important are 
the arch, the strut, and the tie beam or brace. 

202. The Arch, Fig. 65, is formed of blocks placed on 
an arc, either of a circle, or of an ellipse, and the separate 



pieces are held in position by one let in from above (A, Fig. 
65) called a key. Rightly proportioned, it 
is the strongest possible arrangement of 
materials to bear a crushing weight, for the 
load is so distributed as to be perpendicu- 
lar to each block, and it maintains its po- 
sition until one is crushed. It finds its 
application in stone bridges; sewers, and 
Fig. 65. other underground structures; and over 

windows and doors in buildings constructed of masonry. 

203. The Strut is a timber placed so as to change a 
transverse strain into a crushing force, AB 

■ Fig. 66. It gives strength to a structure 
because it prevents bending. It is used un- 
der beams supported at one end, in trestle 
work, and in other positions where the load 
tends to produce deflection, that is to bend 

Fig. 66. 

the beam downwards. 

204. The Brace. Most frame structures are built in the 
form of parallelograms. This renders the structure weak, 

since parallelograms of different 
area, or having different angles, 
may have the same sides. To 
remedy this, a timber is placed 
across the corners, ab and cd, Fig. 
67, thus making triangles, which 
cannot change their angles and 
Fig. 67. retain the same length of sides. 

Such braces should be placed across all corners, whenever 


205. The brace acts sometimes by its elasticity of trac- 
tion and sometimes by its elasticity of pressure. Thus, if a 
beam be braced both above and below, the upper brace ; will 
act by the former, while those below will act by the latter. 

206. The strongest form of frame work is illustrated by Fig. 68. 


A B is the beam to carry the load. 
Timbers AD and BE are firmly 
bolted to its ends, and the upper 
ends of these timbers are connected 
by a beam DE. DC and EF are tie 
rods holding the beam AB to DE. 
Fig. 68. If now a load be placed anywhere 

upon AB, the principal part of that load will be sustained by the 
tie rods, which act by elasticity of traction. Then it is transferred 
by the timbers AD and BE to the ends of the beam, where it tends to 
lengthen the timber, and is again resisted by elasticity of traction. 



207. The first effect of varying the relative strength of 
the two sets of forces, the attraction and the repulsion, 
acting upon a solid, is to change its volume. An increase 
of the repulsive force, or its equivalent, a diminution of 
the attractive, produces expansion. If this continues, at 
a certain definite point, called the melting point,* the co- 
hesion is nearly overcome and the body becomes a liquid. 

208. In the liquid state, the two forces nearly balance, 
and this gives rise to some properties peculiar to this state, 
and to some uses to which liquids may be appropriately 
applied. Liquids also may be employed at rest, or in mo- 
tion. Hence Mechanics of Liquids considers four general 
subjects: the General Properties of Liquids; Specific Grav- 
ity, or the relation of the density of the different bodies; 
Hydrostatics, or the Laws of Liquids at Rest; and Hy- 
draulics, or the Laws of Liquid Movements. 

Section I. — General Properties of Liquids. 

209. The most marked feature of a liquid is the ease 

tSee Heat, Section 514. 



with which the molecules move. Indeed, each molecule of 
a liquid yields to the least external force, moving in a 
straight line in the direction in which the force acts. 

210. This occurs because the attractive and repulsive 
forces are nearly balanced. Were they exactly equal, a 
molecule thus moved would continue its forward motion 
until stopped by some force external to the liquid. But 
liquids have some cohesion, so that the forward motion of 
the molecule is constantly retarded and ultimately overcome. 
That is, all liquids possess a certain degree of viscosity. 

211. This property indirectly effects the production of 
waves. For any molecule moving 
forward must disturb those to ach- 
ing its sides, and thus set up back 
and forward motion among them, 
that is produce waves. 

212. Compressibility and Elasticity. 

Liquids were formerly considered in- 
compressible. That they are not strict- 
ly so is shown by the Piezometer, Fig. 
69. This consists of a glass cylinder, 
A, containing the liquid to be com- 
pressed, with a fine tube, the end of 
which, 0, dips beneath the surface of 
mercury. This is then placed in a 
strong glass cylinder, which is then 
filled with water. At the top is a screw, 
which moves a piston downward. As 
the screw advances, the water in the 
cylinder by Pascall's law* carries the 
pressure to the mercury which rises 
in the tube O, thus compressing the 
liquid in the cylinder A. A Manome- 
ter, B,f is frequently used to show the 

Fisr. 60. 

*See Section 23C. 
tSec Section 327. 


By this means, a pressure of twenty-four atmospheres 
has been found to diminish water about eleven thousandths 
of its volume. When the pressure was removed, the water 
resumed its original bulk. Hence it is inferred that liquids 
are perfectly elastic, at least within the limits of experiment. 

Section" II. — Specific Gravity. 

213. Since all bodies contain pores, to determine the 
relative amount of matter that they contain, they must be 
compared with some substance adopted as a standard. 
Pure water at the temperature of 4° is taken as this stand- 
ard, and the relation of a bodij to water is its Specific Gravity. 

214. Archimedes 9 Principle. The weight of a body 
immersed in water is diminished by an amount equal to 
the weight of the water which it displaces. If lighter 

than water it floats, a part being below 
the surface, while the water rises in the 
containing vessel. Fig. TO shows this, 
for the glass vessel being filled so that 
the water stands exactly at the mark 
upon the tube, the immersion of the 
floating ball causes the water to rise in 
Fig. to. the tube. Drawing out just enough to 

bring the water to the mark again, it is shown to be the 
amount displaced by the ball by removing the ball and 
pouring the water back. 

215. If heavier than water, the body sinks, but loses a 
part of its weight. This is called Archimedes! Principle* 

*The tradition of its discovery is as follows : King Hiero gave some work- 
men the material for a golden crown. Upon the completion of their work, 
they returned him a crown of equal weight. But suspecting it to be alloyed 
with silver, he gave it to Archimedes to determine. After studying the prob- 
lem for some time, he visited the baths when the vessel was completely full. 
Plunging in, he noticed the overflow of the water, and at once thought of ap- 
plying the principle to the crown. In his eagernes, he did not stop to dress, 
but ran through the streets shouting, "I have found it" and detected the 
fraud of the workmen by its greater volume. 



from its discoverer, the celebrated physicist of Syracuse. 

216. Archimedes' Principle is proved by the appa- 
ratus of Fig. 71. A cylinder, which just fits a bucket, 
is attached to a hook at its bottom: and the bucket 
and cylinder are then attached to the arm of a bal- 
ance. Weights are now placed in the opposite scale 
pan just equal to the weight of the cylinder and buck- 
et. Upon immersing the cylinder in water, the 
weights descend ; but filling the bucket with water 
restores the equilibrium. This principle is import- 
ant since the method of determining specific gravity 
depends upon it. 

217. This principle furnishes a ready means of deter- 
mining the volume of a body. All that is necessary is to 
suspend the body by a fine thread, in distilled water of the 
temperature of 4°, its weight being already found, and 
weigh it once more. The loss of weight in water is the 
weight of the water which it displaces, and this is its vol- 
ume in cubic centimetres, since one cubic centimetre of 
water weighs one gramme. 

218. The Cartesian Diver. A body heavier than water 
will sink; of the same weight, will remain in any position; 
and lighter, will rise. 

The Cartesian Diver, Fig. 72, shows these phenom- 
ena. A small porcelain figure is attached to a globe 
which has a small hole on the under side. Water, 
almost sufficient to make the image sink, is placed in 
the globe ; and the image is then placed in a tall cyl- 
inder of water, and a rubber cap tied over the top. 
The image now floats. By pressing slightly upon the 
rubber, a little water is forced into the globe, and the 
image sinks. Eemoving the pressure, the water es- 
capes and the image rises again. 

219. Fishes are enabled to rise to the surface 
of the water by expanding a small sack of air 
Fig. 72. near their back, called the swimming bladder. 
Compressing it, they descend. 


220. The human body is slightly lighter than water, 
and so will float. But the head is heavier than the lower 
parts of the body, and so is kept above the surface only by 
an effort. Hence swimming is an art. But in animals? 
the head is lighter, and floats naturally. 

221. Determination oi Specific Gravity. The specific 
gravity of a body is found by dividing the tveight of the 
body by the tveight of an equal volume of ivater. The only 
difficulty lies in obtaining the weight of an equal volume 
of water. Hence the method differs somewhat with the 
state of the body. 

222. First, Specific Gravity of Solids. Solids are of two 
general classes: those heavier than water and those lighter. 
To obtain the specific gravity of a body heavier than water, 
weigh the body in the air,* and then suspended by one arm 
of the balance, in water; find the difference, which gives 
the weight of an equal volume of water; and divide the 
weight of the body by this. 

223. To obtain the specific gravity of a body lighter 
than water, it must be made to sink by some solid whose 
weight both in air and in water is known. Then sub- 
tracting the weight of the two bodies in water from the 
sum of their weights in air gives the weight of the volume 
of water equal to both. Subtracting from this the loss of 
weight of the heavier body gives the weight of the water 
equal to the lighter body, and dividing the weight in air 
by this gives the specific gravity, as before. 

224. Second, Specific Gravity of Liquids. This is deter- 
mined in two principal ways, by the Specific Gravity Bot- 
tle, and by Hydrometers. 

*Strictl5", in a vacuum. 



225. The Specific Gravity Bottle, Fig. 73, is a 
glass bottle whose weight is known, which holds 
100 grammes of distilled water at the temperature 
of 15°. It is filled with the liquid whose specific 
gravity is required, and weighed, care being taken 
to fill it at 15°. Subtracting the weight of the bot- 
tle gives the weight of the liquid, and dividing by 
100 gives the specific gravity. 

226. Hydrometers are of two kinds, those 
of constant volume, and those of variable vol- 
Fig. 73. ume. 

227. Fahrenheit's Hydrometer is the best of the 
first kind, Fig. 74. It consists of a glass cylinder 
carrying a small bulb of mercury at the lower end, 
and a scale pan at the top supported by astern. A 
mark is made upon the stem to which it is always 
immersed. Its weight is carefully determined. It is 
then placed in water and weights added until it sinks 
to the mark. The sum of the weights in the pan and 
the weight of the hydrometer is the weight of the 
displaced water. Then immersing it in the liquid 
whose specific gravity is desired, the weight of the 
Fig. 74. amount displaced is found in like manner. Dividing 
the last by the first gives the specific gravity. 

228. Baumes' Hydrometer, Fig. 75, shows the 
principle of those of variable volume. It consists 
of a glass stem which carries two bulbs near its 
lower end. The upper one is hollow, and the 
lower is filled with mercury, so that the instru- 
ment always stands perpendicular to the surface 
of the liquid. 

229. Baumes' Hydrometer is graduated ar- 
bitrarily, hut in different ways for liquids 
heavier than water, and those lighter. For 
those heavier, the point to which it sinks in 
water is marked zero. A solution of 15 parts 
of common salt in 85 parts of water is then 

Fig. 75. made, and the point io which the hydrometer 


sinks in that is marked 15°, and the lower part of the stem 
is then divided into spaces of the same length. 

230. For liquids lighter than water, the point where it 
stands in water is marked 10°, and the point to which the 
instrument sinks in a solution of 10 parts of salt in 90 parts 
water is marked 0°. The space between is divided into ten 
parts, and the divisions continued to the top of the stem. 

231. To use the instrument, it is plunged into the liquid, 
the degrees where it stands read from the stem, and the 
specific gravity is then found by Baume's Tables.* The 
instrument is not very accurate. 

232. Modifications of the hydrometer specially adapted 
for use with milk are sold as lactometers. Little reliance 
can be placed upon them as a test of purity, since cream 
is lighter than milk, and even if water has been added, a 
little salt restores the specific gravity. 

233. Third. Specific Gravity of Gases. Gases are so 
much lighter than water that if compared with it, the spe- 
cific gravity would be inconveniently small. Hence they 
are compared with air, or in Chemistry with hydrogen. 

234. To obtain the specific gravity of any gas, a glass 
flask is first weighed when full of air, then when it has 
been exhausted so as to produce a vacuum. The difference 
is the weight of the air in the flask. It is then filled with 
the gas whose specific gravity is required, and weighed. 
The difference between this weight and that of the empty 
flask is the weight of the gas, which, divided by the weight 
of the air, gives the specific gravity. 

*See Table IV, at the end of the volume. 

N. P. 5. 



1. Section" 217. A body whose weight is 22.704 grammes, 
loses exactly 2 grammes in water. What is its volume ? 

2. Section 222. A piece of gold weighing 10 grammes, 
weighed 9.484: grammes in water. What is its specific 
gravity ? 

3. A body weighs 7.55 grammes in air and 5.17 grammes 
in water. Required its s. g. 

4. Section 223. A mass of iron ore weighs 6 lbs. in air 
and 4 lbs. in water. Determine its s. g. 

5. The ore of problem 4 and 1 lb. of cork together weigh 
3.8 lbs. in water. What is the s. g. of the cork? 

6. Determine the volume of a mass of ice of which 439 
cubic centimetres float above the surface of the water, the 
s. g. of ice being .93? 

7. Required the weight of the ice. 

8. Section 225. A specific gravity bottle whose weight 
is 50.9 grms. weighs 150.934 grms. when filled with milk. 
What is the s. g. of the milk? 

9. The same bottle filled with sulphuric acid weighs 
233.1 grms. Determine the s. g. of the acid. 

Section III. — Hydrostatics. 

235. Hydrostatics treats of the laws which apply to 
liquids in a state of equilibrium. Those that are peculiar 
to liquids result from their perfect elasticity. Pascal's 
haw is the most important, named from its discoverer. 

236. Pascal's Law may be determined experimentally 
by the apparatus of Fig. 76. A strong vessel which has five 
pistons of equal areafitting tightly, is completely filled with 



Fig. 76. 

water. If then any given weight, 
as 100 grammes, be placed upon 
one, that will descend, and the 
others move outwards. But an 
addition of 100 grammes to each 
restores the equilibrium. Hence 
liquids transmit pressure equally 
in all directions, and the force 
acts at right angles to the surface 
at any point. 

237. An apparatus consisting of a large globe with sev- 
eral jets shows the same principle. It is filled with water 
and an attached piston is then forced in, and the water is 
driven out of all the jets equally. 

238. Formula. The formula is determined 
by the apparatus of Fig. 77. P and p are two 
pistons of known area resting upon water in 
] two connected cylinders. Weights are then 
added to each. But those added to the larger 
Fig. 77. are as many times greater than those placed 

upon the smaller as the area of one exceeds that of the other. 

For example, if the area of the large piston is ten times 
the smaller, then 100 grammes on P are balanced by 10 

grammes upon p. Hence 
representing the weights by 
P and p, and the surfaces bv 
Sands, |=f orP= 


Fig. 78. 

239. Bramah's Press, Fig. 78, 
is a practical application of these 
principles. It consists of a large 
cylinder, in which is a piston 
moving water tight. This pis- 
ton carries the weight to be 
raised, or the material to be com- 
pressed. A pipe connects this 
with a small cylinder, in which 



moves a piston operated by a lever. Water is supplied to the 
small cylinder from a reservoir, so that it can be forced from the 
small cylinder to the large, and the apparatus converted into an 
hydraulic press. The conditions of equilibrium are given by the 
formula of the last paragraph. 

240. The collar was devised by 
Bramah, Fig. 79. It consists of a piece 
of thick leather soaked in oil, made 
with the cross section in the shape 
of an inverted U. This is placed near 
the top of the large cylinder, and 
Fig " 79, while allowing the piston to move by 

it, prevents the escape of water, for as the pressure upon the un- 
der side increases, the collar presses against the piston with greater 

241. This press is used in raising locomotives; in ex- 
pressing oil from seeds; in pressing books; in making a 
compact mass of sheets of paper for car wheels; and 
wherever great pressure is required. 

242. Pressure produced by Gravity. Gravity causes all 
liquids to press upon the various layers, and upon the con- 
taining vessel, in proportion to the density of the liquid. 
So also, by Pascal's law, the pressure upon all parts of 
the same horizontal layer is the same. 

243. The Upward Pressure of liquids is shown by 
the apparatus of Fig. 80. A glass tube open at the 
ends, has a tightly fitting disc which is held in place 
by a string. When the apparatus is immersed in wa- 
ter, and the string released, the disc is held in place. 
Pouring water into the tube, the disc falls when the 
weight of the column of water in the cylinder added 
to the weight of the disc equals the pressure upward, 
or the downward pressure of a column of water of the 
same area and height as the immersed portion of the 

Fig. 80 

tube, Sometimes a little more is needed because of adhesion. 

244. The pressure upon the side of a vessel at any point 
is readily seen to be that upon any point of a horizontal 
layer at the same distance below the surface. 



245. These facts are -well illustrated by the 
hydrostatic bellows, Fig. 81, consisting of two 
boards connected by leather, so as to be water 
tight. A tube is fixed at one side. Water poured 
into the tube presses downward according to 
its height, and since liquids transmit pressures 
equally, the pressure upon each equal portion 
of the area of the bellows equals that in the 
tube. So a small amount of water will raise a 
heavy weight. 

246. Upon this principle, a small amount 
of water will suffice to burst a barrel. 
The cask is filled with water, and a small 
tube forty or fifty feet long is inserted and 
filled with water. The pressure of the 
column bursts the barrel because trans- 
mitted to all parts of the inner surface 
equally, according to Pascal's law. 

Fig. 81. 

Fig. 82. 
in the tube and in the funnel. 

247. The pressure 
is independent of the 
shape of the vessel. 

This is readily proved 
by a tube, Fig. 82, bent 
twice at right angles with 
a funnel attached to one 
end. Pouring water into 
the funnel, it fills the in- 
tervening tube and comes 
to rest at the same height 
So with the smaller tubes. 

248. The Hydrostatic Paradox. The weight of the liquid 
in a containing vessel determines the pressure of the vessel 
upon its support. But the pressure upon the bottom of 
the vessel is in no way affected by the mass. This depends 
entirely upon the area of the bottom and the height of the 



upper surf ace oi the liquid above the bottom. Hence the 
pressure upon the bottom and upon the support may differ 
very materially, or they may be equal. 

This is well shown by the appa- 
ratus of Fig. 83. A funnel shaped 
vessel is screwed to the top of a 
cylinder the bottom of which is 
closed by a metal plate held in 
place by the arm of a balance. 
Weights are placed in the opposite 
scale pan, not shown in the figure, 
until equilibrium is reached. The 
height of the liquid is marked by 
a stand; the funnel shaped vessel 
is then replaced by the others in 
turn, and the same weights produce 
equilibrium as before, though the 
That is the pressure upon the 

Fig. 83. 

entire mass of liquid is much less, 
bottom is determined by the height. 

249. Reservoirs. A reservoir is a structure of earthwork 
or masonry to hold a supply of water. Since the pressure 
against the structure results from gravity, it will stand 
when its weight equals the pressure. Eeservoirs are use 1 
as embankments of canals, and also to hold a supply of 
water, and their shape varies with their use. 

250. Determination of Form. Since the pressure upon 
the top layer is zero, and upon the lowest is 
due to the entire depth of the liquid, the 
entire pressure may be considered as con- 
centrated at P, Fig. 84, a point one-third 
from the base, that is on the same horizontal 

Fig. 84. } me w ith C, the centre of gravity of the sec- 
tion of the reservoir. But nothing is required to balance 
the upper layer. Hence the section of the side of the 
reservoir must be a triangle. Since the weight of the tri- 
angle alone resists the pressure, it will all be concentrated 
at its centre of gravity C. It must then be equal in weight 



Fig. 85. 

to the pressure of the water, else it will be 
pushed aside. But the factor of safety de- 
mands its multiplication by three. Hence 
the true form is found by placing a par- 
allelogram whose base equals that of the tri- 
angle in addition to it. Fig. 85. 

251. Practically, reservoirs are constructed of earth. 
Hence while the side exposed to the water should be, 
theoretically, perpendicular, it must be so inclined as to be 
stable and resist the wear of the water. Hence the form 
will vary materially with the nature of the earth used in 
its construction. When the embankment rests upon very 
hard soil, the base should be let down into that to prevent 
any possibility of slipping. Most soils require puddling, 
that is pounding, so that water cannot penetrate them, and 
so dissolve out parts of the earth and weaken the structure. 

252. If the water is ever to pour over the top of the 
structure, as in the case of a dam across a river liable to 
considerable increase in volume, the side away from the 
water must be so arranged as to prevent the water from 
ever striking it as it falls. This is accomplished either by 
making the face of the structure perpendicular, or so in- 
clining it that the water can flow quietly down the plane. 
The upper side must also be inclined so that logs and masses 
of ice shall strike at an angle and " glance, 11 or be reflected 
off, in place of giving their momentum to the structure. 

r 253. Equilibrium in Connected Tessels. When vessels 

of different shape and 
size are connected, the 
liquid contained in them 
will stand at the same 
level in all, because the 
downward pressure is the 
Fig. 86. same. Fig. 86. Pouring 



water into any one of the vessels connected by the tube, 
the liquid rises to an equal height in all.* 

254% Upon this principle, cities are supplied with water. 

A reservoir A, Fig. 87, is constructed upon an elevation, and 
connected by an underground pipe B with the place where the 

Fig. 87. 

water is required, as the house D. Then since water is in equi- 
librium at the same level, it rises as high as the reservoir. So 
rivers may be crossed readily by laying the pipe underneath the 
water upon the bed of the stream, as shown at B. A fountain is 
simply an upward jet made by inserting a small pipe perpendicu- 
larly into the main pipe. 

255. Equilibrium of Different Liquids. When liquids 
of different density are used, they will stand at different 

Thus, if a tube bent twice 
at right angles, Fig. 88, be 
filled a little by the bend 
with mercury, and water be 
poured into the branch A to 
the height of thirteen cen- 
timetres, the mercury will 
rise in the other tube B 
only one centimetre. But 
mercury is thirteen times as 
dense as water. Hence these 
liquids furnish the same 

Fig. 88. 

256. A Leyel Surface 

is presented by a liquid 

*Practically, a little difference is noted, due to capillarity. 



at rest. This is not a plane, but since all parts are acted 
upon by gravity equally, it must be curved to correspond 
with the earth. 

257. Leveling is the process of determining a horizontal 
line, or a plane surface. The water level is a long tube bent 

twice at right 
angles, and 
water is made 
to stand at the 
same level in 
both arms, as 
in Figure 89. 
Then by look- 
ing along the 

Fig. 89. 

surface of the liquid in the two tubes, a straight line is found 
which reaches the staff held by an assistant, and the true 
curve can be calculated from this. 

258. A Spirit Level, Fig. 90, is more delicate than a wa- 
ter level. It consists of 
a tube slightly curved, 
nearly rilled with alco- 
Fte- 90 - hoi and sealed. Wlien 

it is level, the bubble of air remaining is in the middle; 
and it may be attached to any instrument. 


1. Section" 239. A Bramah's Press has a large cylinder 
of 1 ft. in diameter, and a small cylinder whose area is 1 
sq. in. The handle is 3 ft. long, and the piston is attached 
4 in. from the end. What weight upon the large piston 
can a man weighing 150 lbs. raise? 

2. Supposing the small piston can descend 6 in., how 
many times must the handle descend to raise the weight 
1 inch? 


3. Section 245. Given a square bellows 1 ft. on each side, 
and a tube 1 inch in area, how high a column of water 
will be required to raise 200 lbs., considering a cubic foot 
of water to weigh 62 lbs. ? 

4. Sectiok 255. The specific gravity of nitric acid being 
1.5, how high a column will be required to balance a column 
of water 9 centimetres high ? 

5. A column of water 30 ft. high is balanced by alcohol 
of .8 s. g. Required its height. 

Section IY. — Hydkatjlics. 

259. Hydraulics treats of the phenomena connected with 
liquids in motion. The movements of liquids may be con- 
sidered in themselves, as influenced by the containing 
vessel and the opening whence they escape : or the moving 
liquid may be employed as a means of producing motion: 
or its movements may be a hindrance to objects moving 
through the liquid. 

260. Jets. If an opening is made in a vessel containing 
water, the liquid flows out. This is called a jet. Its direc- 
tion may be downward, to one side, or upward. 

261. The Contracted Tein. Making an opening removes 
the pressure from that part of a vessel, and produces un- 
equal pressure upon the molecules of the liquid, so that 

they move towards the orifice in all direc- 
tions. Fig. 91. The inertia of the mole- 
cules causes them to continue in the same 
direction after reaching the orifice, so that 
their paths cross in all directions. This 
makes the smallest part of the stream, not 
Fig. 9i. a j. ^ e or ifi ce itself, but a little beyond it, 

and the amount of water discharged is determined by the 

area of a section at this point. 



Fig. 92. 

262. The amount of the flow is somewhat 
increased by inserting a short tube. Its best 
shape is that of the contracted vein. 

263. A Jet Downward. If the orifice be 
in the bottom of the vessel, Fig. 92, the 
stream seems to diminish for a certain dis- 
tance and then to increase in size again. 
This is repeated several times until the stream 
finally breaks up into separate drops. This 
separation is caused by the acceleration of 
gravity upon the molecules, causin^them to 
increase their rate of motion according to 
the laws of falling bodies. 

264. Jets from the Side. If an opening be made in the 
side of a vessel, Fig. 93, the liquid 
will start out horizontally. It is 
then acted upon by its inertia, 
which carries it forward in a 
straight line ; and by gravity, a 
constant force drawing it perpen- 
dicularly downward. The result 
is that the stream is turned down- 
ward, and soon reaches the level 
Since gravity is constant, the 

Fig. 93. 

of the bottom of the vessel. 

shape of this curve must be that of any projectile, or a 


265. If an orifice be made at any given distance from 
the top, and another at the same distance from the bottom, 
the liquid from both will strike at the same point. The 
upper starts with a velocity due to its distance from the 
top, and has a long distance to fall, while the lower jet has 
much greater velocity, but a short distance to fall. A jet 
in the middle sends the water to the greatest distance, for 
it combines inertia and gravity equally. 




266. The volume discharged from any given orifice is due 
to the pressure at that point. Since this varies with the 
depth the greatest volume will be obtained 
from the lowest of several orifices. 

267. If the orifice have a bent tube placed 
in it so that the opening be upward, Fig. 
94, the jet will throw the water nearly to 
the height of the liquid in the vessel. 
That it does not reach the surface is due 
to the friction of the orifice, and the re- 
sistance of the air. 

Fig. 94. 

268. Springs. As water falls upon the surface of hills 
and mountains, it trickles through the surface soil until it 
reaches a stratum of earth that it cannot enter. It then 
flows along this impermeable stratum, constantly descend- 
ing. If the stratum comes 
to the surface at any point, 
as the stratum a does at S, 
Fig. 95, or so near the sur- 
face that the water can break 
through the soil, it flows 
out, forming a spring. 


Fig. 95. 269. A Well is simply an 

opening made to such an underground current of water. 
The water then flows in, filling the well to a point as near 
the surface as the pressure of the water will raise it. 

270. Artesian Well. If the water enter a porous stratum 
situated between two impervious strata, as a, between b 
and 6, Fig. 95, it will then completely fill such a layer, and 
rise on each side as high as its source. By boring a hole, 
and inserting a tube, the water will rise in the tube and 
flow from the surface, as at W, forming an Artesian Well* 

*So named from Artois, in France where they were first employed. 



Fig. 96. 

271. The Hydraulic Ram, Fig. 96, is 
an instrument for raising a portion of 
a moving "body of water by means of 
the momentum of the 'mass. It con- 
sists of a reservoir of water A and a 
dascending pipe B with the end E 
bent upwards. At the lower end Ea 
valve is placed, closing upward, of 
such a weight that it remains open when the water is at rest, but 
closes when it has acquired a little momentum. An air chamber 
D is connected to the descending pipe B by a valve opening up- 
ward, and has a small delivery pipe F opening from its lower part. 

272. The action of the ram is as follows : the water 
flows through the pipe B until it has acquired sufficient 
momentum to close the valve at E. This suddenly stops 
the motion of the end of the mass, but the momentum of 
the portion in the tube raises the valve in the air chamber, 
and forces in some water, compressing the air. As soon as 
the water has all stopped, the valve E falls, and the op- 
eration is repeated. After a short time, the water rises in the 
escape pipe, and flows from the end in a continuous stream. 

273. This instrument will raise one-sixth of the water 
passing through it about ten metres for every metre of fall 
in the main pipe, neglecting friction. 

274. Water Wheels. Machines moved by the momentum 
of running water are called Water Wheels. The most im- 
portant are the Undershot, the Overshot, the Breast, and 
the Turbine. 

Fig. 97. 

275. TheUndershotWheel,Fig.97, 

consists of a wheel carrying a series of 
floats, called buckets, attached to its 
rim, which dip into the water. The 
water flows beneath the wheel, and 
acts by its momentum. This wheel 
will utilize about thirty per cent, of the 
force of the water. 



Fig. 98. 

276. The Overshot Wheel, Fig. 98, has the water sup- 
plied by a spout which passes over 
the wheel. It then pours into 
buckets of such a shape that the 
water is held until the bucket de- 
scends past the centre of the 
wheel, and these buckets must be 
sufficiently shallow to allow all 
the water to be poured out before 
the bucket begins to ascend. The 

water acts principally by its weight, and with this wheel 
seventy per cent, of the force has been used. 

277. The Breast Wheel, Fig. 99, utilizes both the mo- 
mentum and the weight of the wa- 
ter. It consists of a wheel fitting 
closely to a race-way, and the water 
pours over the dam at a point as low 
as the centre of the wheel. The 
wheel is carried forward by the mo- 
mentum of the water as it pours 
into the race-way, and the weight of 
the water adds to the rate of motion. 

This wheel is less effective than the overshot, but can be 
made twice its diameter. 

Fig. 99. 

278, The Turbine is the most effective water wheel that 
has yet been devised. In some well conducted experiments 
at Lowell, Mass., it utilized about ninety per cent, of the 
power of the water. Of course, in practical use, the wheel 
falls far short of working with so small a loss as is indi- 
cated here, but making all due allowances, it will utilize 
about twice as large a proportion of the water's power as 
either of the other wheels. 

279. The experiment of Fig. 100 illustrates the principle 
of the Turbine wheel. 



A tall glass cylinder nearly filled 
with water V and having a stop- 
cock at L is floated upon the sur- 
face of water. So long as the stop- 
cock is closed, the cylinder remains 
stationary: opening the stopcock, 
the water pours out, and the cyl- 
inder slowly moves away from the 
stream. The pressure at first was 
equal in all directions; after open- 
ing the orifice, the pressure upon 
that side was diminished by the 
Fig. loo. amount due to the area of the open- 

ing, while that on the opposite side remained the same. Hence 
the greater pressure causes motion in its direction. 

280. Barker's Mill, or the reaction water wheel, is a 
modification of the above experiment. Fig. 101. It con- 
sists of an upright tube through which 
the water ascends, supplied from a spout 
which passes underneath the wheel, and it 
carries a horizontal tube at the top, with 
the ends bent in opposite directions. The* 
pressure of the water upon the closed side 
of the tube exceeding that upon the other side by the 
amount due to the area of the opening drives the tube 
backwards away from the opening. 

Fig. 101. 


large n 

In principle, • the Turbine Wheel, Fig. 102, is a 
umber of tubes united together. It consists of a 
central portion GH divided into 
compartments by curved parti- 
tions, into which water flows from 
a flume. A rim AB is divided 
into compartments by partitions, 
c, d, e, f, curved in the opposite 
direction to those which form the 
central portion. The rim is fast- 
ened to a plate which forms the 
Fig. 102. bottom or top of the wheel, and 


the plate is also attached to the shaft I. This rim, plate and 
shaft turn together, while the central partitions do not 
move. The water pours into the central portion, and flows 
thence to the rim, where it strikes the curved partitions at 
right angles and is stopped. Thence it falls through the 
bottom of the wheel by its own weight. 

282. Machines Movicg through the Water. The most 
important of these are the Paddle Wheel, and the Screw 
Propeller, or Stem Wheeler. 

283. The Paddle Wheel consists of a wheel with float 
boards set in the rim, and is placed at the side of a steam- 
boat. It is driven by machinery within the boat, and 
propels the boat because the water resists its movement. 
If the water was a solid, its rate of motion would deter- 
mine the motion of the vessel. Since water is a liquid, it 
3 T ields to the force of the wheel, and moves backward, so 
that the rate of motion of the boat is the. difference be- 
tween the backward motion of the water and the distance 
traveled by any point of the wheel's rim. 

284. The Screw Propeller is a short screw placed at the 
stern of the boat. The water acts as the nut, and the ves- 
sel's rate of motion is the difference of motion of the screw 
and the water. The screw itself revolves, driven by means 
of a crank attached to the engine. The threads, usually so 
short as to make only a small part of a single turn, are 
three or four in number, and the ease with which the water 
moves away from them causes them to lose much of their 
efficiency. The screw is placed so as to be just below the 
surface of the water. Nearly all ocean steamers are now 
driven by the screw, and are usually known as stern wheelers. 





285. When the repulsive force has so increased as to 
exceed attraction, cohesion is overcome and the body be- 
comes a gas. The distinctive properties of gases result 
from the excess of repulsion. The most important are 
Unlimited Expansibility, and Compressibility. 

286. The Expansibility of gases may be shown by 

placing a small bolt head, Fig. 103, containing 
a little air, under the receiver of an air pump* 
and exhausting the air. The air in the bolt 
head expands and nearly fills the bulb and 
tube, so expelling the water in it previously. 

287. Expansion is without limit, for if 
Fig. io3. a receiver be exhausted as completely as possi- 
ble, the small amount of air remaining fills every part. 
Or, if a large receiver be exhausted and a small nask of 
some colored gas be opened in it, the colored gas may be 
seen in every part of the receiver. 

288. A variety of experiments may be performed that 
depend upon expansibility. A shrivelled apple covered 
with a receiver and the air exhausted, becomes distended. 

289. If a minute hole be made in the small end of an 
egg, and the egg be then placed, hole downward, in a coni- 
cal glass, upon exhausting the air, the egg will be forced 
out of the shell through the hole. When the air is read- 
mitted, nearly all the egg will be forced back into the shell. 

*See Section 300. 
N. P. 6. 


290. The Force of expansibility may be shown by tak- 
ing a cube of thin glass, corking the neck 
tightly, covering it with a wire cage to pre- 
vent accident, and placing the whole under a 
small receiver, Fig. 104. Exhausting the air 
reduces the cube to fragments. 

.291. The kinetic theory furnishes an ex- 
rig. 104. planation of the expansive force of gases. 
Each molecule of a gas is moving forward, according to 
the first law of motion, with inconceivable rapidity.* So 
long as the pressure of the gas is the same upon both sides 
of any vessel, its inner and outer surfaces both receive the 
same number of blows from the moving molecules in any 
given time, as one second. But exhaust the air from one 
side, and that surface receives a much less number of blows, 
and this difference cf mechanical work done by the moving 
molecules is manifested by the difference of pressure, so 
that an exhausted body is pressed inwards by the surround- 
ing air. Were the exhaustion perfect, no molecules would 
reach the exhausted surface, but it falls far short of this 
perfection with the apparatus now in use. 

292. On the other hind, gases are perfectly compressi- 
ble, within moderate limits. The fact of compressibility 
is readily shown by pressing an inverted glass vessel down 
into water. The water rises in the vessel by compressing 
the air, in proportion to the distance below the surface. 

293. Gases subjected to great pressure have their elas- 
ticity overcome, and become liquids or solids. In some, as 
chlorine, a moderate pressure suffices. In others, as oxy- 
gen and hydrogen, a great pressure, as much as four hun- 

*On the kinetic theory, "one cubic inch of every gas, when the barometer 
marks ^0 inches, and the thermometer '62° Fahr., contains ten twenty-third 
power molecules. Mean velocity of hydrogen molecules, under the same con- 
ditions, G,097 feet per second."— Cooke's New Chemistry, P. 43. 



dred atmospheres* is required, and to overcome the heat 
produced by the mechanical power used in compression, 
the greatest artificial cold must be employed. 

294. Condenser. The increased elasticity of 
compressed gases may be shown by experiments 
with the Condenser, Fig. 105. 

This consists of a strong cylinder with a solid piston 
fitting air tight. A valve in the lower end closes when 
the piston descends and opens as it ascends. A valve in 
the tube connecting with the chamber opens downwards, 
so allowing the air to be forced out by the descending 
piston, but preventing its return. The 
condenser is screwed into a Condensing 
Chamber, Fig. 106, and the air is con- 
densed by moving the piston back and 
forth. Upon opening a stop-cock the air 
rushes violently out because of its elas- 

295. The force of condensed air is 
Fig. io5. s hown by attaching an air gun with 
a cork in the end, to one of the stop-cocks of the condens- 
ing chamber. Upon opening the stop-cock the condensed 
air forces the cork out. 

296. The pop gun acts in the same way, the piston con- 
densing the air when it is fired. 

297. By attaching a Barker's Mill with 
very small openings, Fig. 107, to the con- 
densing chamber, the escaping air will 
force it around at a rapid rate. 

Section" 1. — The Atmospheke. 

298. The existence and inertia of the air are shown by 
a variety of common experiences. The resistance offered 

*See Section 316. 



in running; the effect of the wind; and the current of air 
produced by fanning are all proofs of the inertia of the air. 

299. The Atmosphere consists of a mixture of about 
four parts of nitrogen with one part of oxygen. Some 
other gases are usually present in small quantities. That 
the air is a mixture is shown, experimentally, by mixing 
the two gases in the above proportion, when the mixture 
will show all the properties of the air. But the decisive 
proof is that water absorbs the two gases from the air, not 
in the proportion in which they make it up, but in the 
proportion in which it absorbs them from the pure gases. 

300. The Air Pump. This instrument, shown in Fig. 108, con- 
sists of a cylinder in which a piston moves air tight. A valve at 
the bottom of the cylinder opens upward, so that air can pass up 

Fig. 108. 
but not return. The piston also has a valve opening upward, 



and an additional valve is often placed at the top to prevent the 
external air from rushing in above the piston as it descends. A 
small pipe connects the cylinder with a metal plate ground so 
that a glass receiver can be placed upon it, and fit air tight, to cover 
any article from which the air is to be exhausted. A thread is usu- 
ally cut in the hole in the plate where the pipe enters, so that 
pieces of apparatus can be screwed to it, as for example, a gallows 
connector to operate the upward pressure apparatus. 

The action of the pump is as follows: as the handle is depressed, 
the piston is raised, opening the valves in the cylinder, and closing 
the valve in the piston. The air in the receiver is then expanded 
to till the space of the receiver and the cylinder. When the pis- 
ton reaches the top and is again dejDressed, the valves at the bottom 
and top of the cylinder close. The air is thus prevented from 
returning to the receiver, and is soon compressed beneath the 
piston sufficiently to open its valve and rush up through the pis- 
ton. In this way, the air is soon exhausted until it becomes too 
rare to raise the valve, when the action ceases. 

301. The Rotary Air Pump. 

Several improvements have 
been made in the air pump late- 
ly which have been combined 
in the Rotary Air Pump, Fig. 
109. In this, the motive power 
is applied to a crank and heavy 
balance wheel, so allowing of 
very rapid exhaustion. Besides, 
the valves are made to work 
automatically by the device 
shown in Fig. 110, which is a 
perpendicular section of the 
piston and cylinder. The valve 
at the bottom is made as a cyl- 
inder with conical head, and a 
rod is attached which moves 
through the piston with just 
sufficient friction. to raise and 
open the valve as the piston 
begins to ascend. When it 
Fig - 109, reaches the top, it touches a 

ever which closes the valve at the bottom of the cylinder before 



the piston descends. Be- 
sides, the valve in the pis- 
ton itself is opened and 
closed by its own motion, 
for as the piston begins 
to descend, the rod is de- 
pressed a little so that the 
air can rush up around it. 
When the piston begins 
to rise, the conical lower 
end of the rod closes the 
opening in the piston. 
By these means, the ex- 
haustion is rendered 
much more complete than 
with the ordinary pump. 

302. The Downward 
Fi *- 110 - Pressure of the air is 

proved by the bladder glass, Fig. 111. This 
consists of a strong receiver open at both 
ends, with a piece of bladder tied tightly over 
one end and dried. The other end is then 
placed upon the plate of the air pump, and 
the air exhausted, when the bladder is forced Fi s- m - 
down by the pressure of the air. At first it bends inward 
from the pressure, and soon it bursts with a loud report. 
If the end is covered with rubber in place of a bladder, the 
rubber will often be bent inward until it fills the glass 
completely. The large end of the glass may also be placed 
upon the plate of the pump, and the small end covered 
with the hand, when the pressure of the air will prevent 
the removal of the hand. 

303. The Upward Pressure is shown by a variety of 
familiar experiments. If a small glass tube be filled with 
water and the upper end closed with the finger, the upward 
pressure of the air will keep the water in the tube. But 
the most convincing way in which it is shown is by the 



Fie:. 112 

weight lifter, Fig. 112. This con- 
sists of a strong glass cylinder 
with a piston fitting air tight, 
which carries a heavy weight, the 
whole being supported by a stand. 
A ground metal plate is placed on 
top, and connected to the air pump 
by a rubber tube. Exhausting 
the air above the piston, the up- 
ward pressure of the air raises the 
piston and weight, and will carry 
an amount equal to as many times 
fifteen pounds as the area of the 
piston contains square inches. 

304. The Magdeburg Hemispheres, Fig. 113, consist of 
two metal hemispheres, whose edges are 
ground so as to fit air tight. A little tallow 
is placed between them, one of them screwed 
to the plate of the air pump by a stop-cock, 
and the other placed upon it. The air is then 
exhausted as completely as possible, and the 
stop-cock closed; they are then removed from 
the pump, and a second handle attached to 
the stop-cock. A considerable force is re- 
quired to separate them, because the air 
presses upon them from all direcctions. It 
is said that a pair of hemispheres two feet in diameter over- 
came the force of eight horses, four pulling in each direction. 

The pressure of the air in all directions has been applied 
to operate brakes for stopping railroad cars very quickly. 
A pair of boards connected by leather or rubber made air 
tight, are ordinarily kept apart by a spring. A tube con- 
nects them with an air pump placed upon the engine, which 
exhausts the air when it is desired to apply the brake. The 
pressure of the air upon the boards forces them together. 

Fig. 113. 



305. A variety of other experiments may be per- 
formed with the air pump, but all depend upon 
the principles already proved. One of the most 
pleasing is the vacuum fountain, Fig. 114. A tall 
receiver with a stop-cock, and jet inside, is screw- 
ed to the pump and the air exhausted. It is then 
removed, the stop-cock placed in a vessel of water 
and opened. The pressure of the air upon the 
surrounding water forces it to the top of the re- 
ceiver in a jet. 

306. The Buoyancy of the Air is shown 
by the apparatus of Fig. 115. A hollow 
globe is accurately balanced 
by a weight of lead. Now 
closing the stop-cock, plac- 
ing this under a large re- 

Fig. 114. 

ceiver and exhausting the air, the globe 
descends, showing that it is now heavier 
than the weights. The reason is that each 
is buoyed up in air by an amount equal to 
the weight of the air it displaces, but as 
the globe displaces more than the bal- 
ancing weight, it loses more weight. 

Fig. 115. 

307. Upon this principle, bodies weighed in air lose a 
part of their weight, and all accurate weighing must be 
done in a vacuum. So also a light body of given weight 
contains more matter than one more dense, but which 
weighed in air seems to have the same weight. Or a gramme 
of feathers is actually heavier than a gramme of lead, be- 
cause the lead contains more matter in the same volume, 
and is to that extent less porous. 

The pores of solids may be shown readily by immersing 
a small piece of pine wood in a dish of mercury, covering 
it with a receiver and exhausting the air. Upon readmit- 
ting the air, mercury enters the pores, and can be seen with 



the eye. A clean cut across the pores with a knife shows 
a surface like silver. 

308. Balloons. The buoyancy 
of the air causes the rise of bal- 
loons. A Balloon, Fig. 116, is a 
pear-shaped sack made of strong 
oiled silk, and filled with some 
gas much lighter than the air. 
Hydrogen is the lightest gas, but 
coal gas is usually employed, be- 
cause much cheaper than hydro- 

309. Since the balloon dis- 
Fig. ii6. places air of greater weight than 

itself, it will rise, and will take with it a car or basket 
carrying considerable weight. A valve at the top can be 
opened by a rope in the car, so allowing the gas to escape 
when the persons wish to descend; and to increase the 
ascent, bags of sand are thrown out, thus diminishing the 
weight carried. The car itself is suspended by a netting 
passing over the balloon, thus pressing upon all parts 

310. The Parachute is sometimes attached, to allow of 
a safe descent in case of accident. This consists of a " large 
umbrella," which by the resistance of the air through 
which it moves, prevents too rapid descent. A funnel is 
placed in the centre, so that the condensed air can pass 
through in place of causing the parachute to rock from 
side to side. 

Balloons were at first inflated by placing a fire under an 
opening at the bottom and allowing the heat to rarify the 
air within. These fire balloons are no longer used because 
excessively dangerous. 



Section II. — Barometers. 

311. Barometers are instruments for measuring the 
downward pressure of the air. Since gases move even 
more readily than liquids, the pressure at 
any point must depend upon the number of 
layers of air above that point. 


312. Torricelli's Experiment. Fig. 117. 
If a glass tube more than 760 millimetres 
long, with one end closed, be filled with mer- 
cury and inverted in a vessel of mercury, 
the mercury will fall, leaving a vacuum in 
the upper part, but will remain in the tube 
to the height of about 760 millimetres. The 
space between B and n represents the vacuum 
This experiment was first performed by Toi- 
ricelli, a pupil of Galileo, and he explained 
the phenomenon. 

313. The mercury is held in the tube by 
the pressure of the air upon the surface of 
the mercury in the vessel, and it leaves a 
vacuum in the top because the weight of the 
column extending to the top of the tube 

Fig. 117 

would exceed the pressure of the air 

314. Pascal's Experiments. To confirm Torricelli's ex- 
planation, Pascal performed two distinct experiments. 
Perceiving that if the air holds the mercury in the tube, it 
must stand at different heights at different places, he car- 
ried the tube to an elevation. As he expected, the mercury 
fell, and the column diminished with the elevation. 

315. Pascal further reasoned that other liquids should 
be held at heights differing inversely as their specific grav- 



ity. Making the experiment with water he found that the 
air would hold a column thirteen times as high as the col- 
umn of mercury. He also tried other liquids, as wine, and 
alcohol, and found the principle correct. 

316. This principle affords a means of determining the 
pressure of the atmosphere. For a column of mercury 
760 millimetres, or 30 inches, in height, 
having an area of one square inch, weighs 
about fifteen pounds. This then, must be 
the weight of a column of air of the same 
area, and extending to the top of the atmos- 
phere. This is called an atmosphere, and is 
often used as a unit in determining pressures. 

317. The Cistern Barometer, Fig. 118, 
consists of a tube closed at one end, and used 
as in the Torricellian experiment. The di- 
ameter of the tube must be nearly one cen- 
timetre, to overcome capillarity, and even 
then the surface of the mercury is slightly 
depressed by this force. The tube must be 
exactly perpendicular, and a scale is placed 
at one side, divided into millimetres, or inches 
and tenths of an inch. A vernier* is also 
added, reading to hundredths of an inch. 
This instrument is liable to error, for differ- 
ence in the height of the mercury in the tube 
causes a difference of level in the cistern, 
which is the zero of the scale. Since the 
variation in the height of the mercury is 
small, the scale is* omitted except near the 
top. A thermometer at the side of the tube 
indicates the temperature. 

Fig. 118. 

*A vernier is made by taking nine or eleven parts, as nine or eleven tenths 
:>f an inch, and dividing the space into ten equal parts. Then each division 
varies one-tenth from the original scale. 



Fig. 119. 

318. Fortin's Barometer is used in 
all accurate work. Fig. 119. It con- 
sists of a tube and cistern, as in the 
cistern barometer, but the bottom of 
the cistern is made of leather, so that 
it can be raised or lowered by a screw C. 
An ivory point a is placed at the top 
of the mercury in the cistern, and be- 
fore reading the height of the barome- 
ter, the mercury is brought by the screw 
exactly to this point. This barometer 
is usually placed in a brass case, and is 
hung by a ring, so that it is always per- 

319. The Aneroid Barometer con- 
sists of a hollow metallic box, the top 
corrugated, from which the air has 
been exhausted. A change, of pressure 
changes the volume of the box. A se- 
ries of levers connects the top of the 
box to an index, and the graduation is 
usually made by experiment, to agree 
with the mercurial barometer. Tins is 
the most delicate barometer known, a 
difference of elevation of one metre 
producing a change in the reading. 

320. Causes of Variation in the Barometric Height. 

The normal pressure of 760 millimetres is the height of 
the barometer at the level of the sea. Hence, going inland, 
the height of the barometer will vary with the elevation of 
the point above the level of the sea. This allows the instru- 
ment to be used in determining the height of mountains 
above the sea level. 

321. Besides this, many causes produce a variation of the 



height at the same place. An increase of moisture in the 
air usually diminishes the pressure and causes the barome- 
ter to fall. Such a change then indicates an approaching 
storm. Sudden variations in the height indicate violent 
currents in the air. These are some of the more important 
causes of variation. 

Section III. — Boyle's Law. 

322. The law which governs the compressibility of gases 
was discovered both by Boyle and by Mariotte. For this 
reason it is sometimes named from one discoverer, and 
sometimes from the other. 

323. Mariotte's Tube, Fig. 120, is used to 
determine the law. This consists of a strong 
glass tube, one end closed, bent in tlie form 
of a U, but with the open arm much longer 
than the other. It is then fixed to a stand, 
which is graduated to millimetres, or feet 
and inches. 

324:. To use the apparatus, mercury 
is poured into the tube so as to seal the 
bend, and stand at zero in both arms. 
This confines the air in the short arm, 
and the pressure is one atmosphere 
upon each. Mercury is then poured 
into the longer arm until the volume 
of the confined air is reduced one-half. 
This is found to be 760 millimetres, or 
one barometric height, so that the con- 
fined air sustains a pressure of two at- 
mospheres. An addition of another 
atmosphere reduces the volume to one- 
third. Hence the law: The volume of 
gases varies inversely as the pressure. 
This can also be readily proved for di- 
minished pressure. 

Fig. 120. 



V J 


325. This law is true for moderate pressures only. If 

several tubes be filled with 
different gases, Fig. 121, and 
great pressure be applied by 
means of a force pump, for a 
time the gases seem to vary 
according to this law. But a 
point is reached with each gas 
bej r ond which it diminishes 
more rapidly than the law de- 
mands. The reason of this 
probably is that the gas is then 
-aV approaching the point where 
it becomes a liquid. Perhaps 
cohesion is already beginning 
Fig. i2i. to act, so adding its force to 

the force of compression. : 

326. Manometers are instruments for meas- 
uring the pressure of confined gases, as steam 
in a boiler. They are of two kinds, Open 
Air, and Compressed Air. 

327. The Open Air Manometer, Fig. 122, 
consists of a long glass tube B placed per- 
pendicular. The lower end is bent into the 
shape of a TJ, and connected with a bulb A 
containing mercury. The tube C connecting 
the instrument with the gas whose pressure 
is to be measured opens above the mercury- 
When the pressure is one atmosphere, the 
mercury stands at the same height in the 
bulb and in the tube. As the pressure in- 
creases, the mercury rises in the tube, each 
760 millimetres indicating an additional at- 

328. The Manometer with Compressed 

Fig. 122. 



Air, Fig. 123, is a strong glass tube full of air, with one 

end closed arid the oth- 
er dipping beneath the 
surface of mercury in 
a strong iron vessel. 
A tube supplies the gas 
whose pressure is to be 
measured, shown in the 
figure connected with 
a powerful condensing 
pump, above the sur- 
face of the mercury. 
When the pressure is 
Fig. i2s. one atmosphere, the 

mercury stands at the same level in the iron cistern and in 
the tube. When the pressure is two atmospheres, the con- 
fined air is reduced to one-half its original volume. Three 
atmospheres reduces it to one-third, and so on, according to 
Boyle's Law. 

329. The Steam Guage, as commonly used to measure 
the pressure of a boiler, consists of a spring attached to a 
closed box. The steam presses against the side of the box 
and bends the spring. A lever and index attached to the 
spring show the amount of bending, that is the pressure. 
The instrument is graduated to agree with the Open Air 

Since the heat of the steam destroys the temper o*the 
spring when it acts upon it directly, guages are generally 
so connected to the -boilers, that a column of cold water 
stands in the connecting pipe. The steam presses upon 
the water, and by Pascal's law, the pressure is transmitted 
to the spring undiminished. The column of water may be 
placed vertically, or in any other convenient position, and 
it may be bent into any desired shape. 


Section" IV. — Apparatus Depending upon Gases. 

330. The principles developed in the preceding sections 
are applied in many different instruments. Only the more 
important are here mentioned. They may act either by 
means of compressed air, or any other gas may be used in 
the same way. Thus, in many chemical works, the acid 
liquids are pumped from one vat to another by closing the 
top and condensing the air above the liquid. This presses 
it into a pipe opening below the liquid. But in the soda 
fountain, the pressure which drives the liquid out is ob- 
tained by condensing carbonic anhydride above the water. 

331. Hero's Fountain, Fig. 124, consists 
of two hollow glass globes whose upper por- 
tions are connected by a tube. A pan con- 
nected with the lower globe by a tube is 
placed above the upper globe. This tube 
should reach very nearly to the bottom of 
the lower globe. A jet is placed in the pan, 
connected with a tube reaching nearly to 
the bottom of the upper globe. The air in 
both globes maintains the same density. 

332. To use the fountain, the jet is un- 
screwed, and the upper globe nearly fill- 
ed with water. The jet is then replaced, 
and water poured into the pan. This 
flows down through the tube into the 
lower globe, so compressing the air in 
that and the upper globe. The elas- 
ticity of the compressed air forces the 
water in the upper globe out through 
the jet. Disregarding friction and the 
resistance of the air, the water will rise 
through the jet to a height above the 
surface of the water in the upper globe 
equal to the distance between the level 

Fig. 124. 

of the water in the pan and that iu the lower globe. 



333. The Siphon, Fig. 125, is a bent tube with one leg- 
longer than the oth- 
er. It is first filled 
with the liquid to 
be moved, or the air 
exhausted, and then 
the shorter leg is 
placed in the liquid. 
The difference in the 
weight of the liquid 
in the two legs caus- 

Yi g . 125. es it to flow from the 

longer leg, and the pressure of the air upon the surface of 
the surrounding liquid keeps the short leg constantly full. 
The short leg can never exceed in length the height of a 
column of the liquid whose weight equals the pressure of 
the air. With water, this is about ten metres. 

334. The siphon is used in transferring acids from one 
vessel to another; in passing liquids into cellars where the 
containing cask will not enter; and in moving water over 
the top of low hills. 

335. The siphon explains the variation in the flow of 
intermittent springs. A cavity in the rock, whose discharge 
is shaped as a siphon, becomes filled with water above the 
bend. The discharge then commences and continues until 
the liquid is drawn below the orifice. It then ceases, to 
commence again when the water has once more risen above 
the bend. In some springs, this only varies the volume. 

336. The Suction Pump, Fig. 126, at the left, is simply 
a rough made air pump, the piston and all the parts being 
made in the same way. The water is raised to the lower 
valve by the atmospheric pressure upon the surrounding 
water. Hence its distance from the surface can never ex- 
ceed ten metres. 

N. P. 7. 



The Forcing Pump, Fig. 126, on the right, raises the 

water to the lower valve 
by the pressure of the at- 
mosphere. The piston is 
solid, and a discharge pipe 
containing a valve open- 
ing upward, is placed at 
one side of the cylinder, 
and opens into it near 
the lower valve. Pressure 
upon the piston forces the 
water up the discharge 

Fig. 126. 


To render the stream continuous, an air chamber, shown 
as a glass globe, is usually added, in which the upper valve 
is placed, and the discharge pipe opens near its bottom. 
The water is forced into this chamber by the piston, com- 
pressing the air, which by its elasticity forces the water 
out in a continuous stream. 

338. The Fire Engine, when worked by hand, is simply 
a double force pump, with a single air chamber, and one 
discharge pipe with narrow nozzle. 

The Steam Fire Engine is a large force pump driven by 
a steam engine. 

The Diving' Bell is a solid iron bell open at the bottom, 
Fig. 127. The water enters underneath until it 
compresses the air to an amount equal to its own 
pressure. The supply of air can be increased 
by the aid of a condenser and supply tube un- 
til the water is entirely forced out from beneath. 
In this way, the earth under water is readily ex- 
posed for examination by the persons inside 
the bell. It is often used in laying the founda. 
tions of bridges, and in submarine masonry. 



340. For a discussion of the nature of the Undulatory 
Forces, see Book II, Chapter II, page 40. They will be 
treated in the following order, Acoustics, Heat, Optics, and 

Past I. — Acoustics. 

341. Acoustics treats of the production, propagation, 
laws and effects of sound. The term sound is used indefi- 
nitely, to mean the sensation which we call a sound, or its 
cause. The two are, however, logically distinct. 

342. A sound is the effect produced upon the ear by 
vibrations of an elastic body, carried to the ear by some 
transmitting medium. Hence, to produce an audible 
sound, all of these must be present. 

The term sound is also used conveniently for the undu- 
lations of the transmitting medium. It is so employed in 
the following discussion. 

343. That vibrations of a sonorous body produce sound can be 
shown by either of the following experiments. Partly fill a glass 
vessel with water ; the surface remains at rest. Cause the vessel 
to give a sound, either by striking it, or by drawing a violin bow 
across the edge, and the water is thrown into waves. 



344. Or, suspend several pith balls exact- 
ly in contact with an empty glass vase, Fig. 
128. Causing this to produce a sound, 
though the vibrations may not be suffi- 
ciently intense to be seen readily, the pith 
balls are always kept at a little distance. 

345. To show the necessity of a 
Fig.. 128. ^ transmitting medium, a bell suspended 

by a string is placed upon the plate of the Air Pump. It 
is then covered by a receiver which has a sliding rod, so 
that the bell can be rung without admitting the air. After 
exhausting, the bell can scarcely be heard. Perfect ex- 
haustion would remove all sound. Hence, without a trans- 
mitting medium, there can be no sound. 

346. The medium by which sound is transmitted may 
be solid or liquid, as well as gaseous. For, placing the ear 
at one end of a long pole, a slight scratch upon the other 
is heard as plainly as though made at the ear itself. Or, 
two stones brought together under water can be heard by 
a person in the water a mile distant. So water pipes filled 
with water have been used as a means of communication 
between places several miles apart, and words spoken at 
one end have been distinctly heard at the other. 

347. That an ear must be present to receive the sensa- 
tion of sound, requires no proof. The essential part to 
receive the sensation is the nerve of hearing, as is shown 
by the audiphone, in which the undulations are conveyed 
to the bones of the head through the teeth and thence to 
the nerve and are heard, as though received by the ear. 

348. The vibrations of the sonorous body produce cor- 
responding vibrations in the transmitting medium, which 
extend in all directions. That is, each vibration in the 
sonorous body develops a similar vibration in the medium 
in every direction. Hence each vibration in the medium 


is a sphere, and a series of successive vibrations becomes a 
series of concentric spheres whose common centre is the 
sounding body. 

349. Effect upon the Medium. The vibrating body pro- 
duces a series of condensations and rarefactions in the 
transmitting medium. This is well shown by considering 
only a small section of the surrounding air, as the amount 
contained in a cylinder. • 

Let P, Fig. 129, represent 
the vibrating body. As it 
moves forward it reaches a, 
compressing the air in front 
to a certain distance, as H. 
Fig. 129. Its elasticity then moves it 

back to its original position, and its acquired velocity carries it to 
an equal distance to the other side, rarefying the air. But the 
condensation continues to move forward at a uniform rate, so 
reaching H' when P reaches A. So there is a condensation at H' 
and a rarefaction at H. This operation is repeated constantly so 
producing a series of condensations and rarefactions. The condi- 
tion of the air in the tube well represents the changes in the 
entire surrounding medium. 

359. Tyndall'sTube. The movement of the molecules of 
air in sound is in the direction in which the wave is mov- 
ing, or longitudinal. This can be determined readily by 
the principles of motion, and the theoretical discussion is 
proved experimentally by TyndalVs Tube, Fig. 130. 

This is a tin tube 
three or four metres 
long, and about one 
decimetre in diame- 
ter, with one end 
Fig. 130. conical. A lighted 

candle is placed so that the axis of the open cone is directed upon 
the flame. Bringing two books in contact at the opposite end 
produces a pulsation, and puts out the flame. That no air is 
driven through the tube is shown by filling it with smoke, none 


of which leaves the tube when the flame is extinguished. Hence 
sound moves by a pulsation. 

Division I. — General Principles. 

351. The principles of Acoustics consider two general 
subjects, the Laws which govern the movements of the 
molecules of the transmitting medium, and the Effects pro- 
duced by interposing some surface. 



352. Sounds moving through a transmitting medium 
differ in two respects : the distance that a single molecule 
moves may vary:, or the rate at which the condensation 
and rarefaction, that is a complete vibration, advances may 
vary. The former determines the intensity of the sound: 
the latter, the velocity. 

Section I. — Laws of Intensity. 

353. The Intensity of a sound varies with the distance 
of the sounding body, the distance to which each molecule 
moves, and the density of the air. It is governed by the 
following laws: 

354:. I. Since sound is a radiant force, and is propagated 
in all directions in concentric spheres, it must vary as the 
surfaces of spheres vary. In other words, the intensity 
of sound varies inversely as the square of the distance of the 
sonorous body. 

355. The law of intensity cannot be readily proved with 
scientific accuracy. But it may be demonstrated experi- 


mentally, so as to indicate the principle involved, by means 
of two bells which give the same note. Let one be placed 
at twice the distance from the ear of the other, and equal 
blows be struck upon each, the nearer one seems much 
more intense than the other. But if the blow upon the 
more remote be four times the intensity of that upon the 
nearer, the ear distinguishes no difference in the intensity 
of the two sounds. 

356. II. The intensity of sound varies as the distance 
that each molecule of the vibrating body moves. This is 
readily shown by vibrating cords of considerable length; 
the further the cord is made to vibrate, the louder is the 

357. III. The intensity of sounds depends upon the den- 
sity of the air. The truth of this is proved by the bell 
under the receiver; as the air is exhausted, the sound be- 
comes more faint. So too, sounds are much less distinct 
upon an elevation than at the surface of the sea. The 
report of a pistol fired upon Mont Blanc does not much 
exceed that of a cracker fired in the valley below. 

358. The intensity of sound varies with the state of the 
air, and the direction of the wind. A sound is always heard 
further in a calm day than when the wind is strong. In 
the latter case, it is heard further in the direction towards 
which the wind blows, than in the opposite direction. The 
presence of visible clouds, or even invisible vapor,* seems 
to affect the intensity of sounds. 

359. Sound too seems to move more readily in air of 
uniform density than in that which is variable. Besides, 
it passes much more readily to that which is less dense 
than to that which is more dense. Nearly all have ex- 
perienced the great difficulty of making persons at the 

♦Tyndall's experiments. 



foot of a hill hear the sound of the human voice, though 
every word spoken by them was heard distinctly. 

360. Means of Strengthening Sounds. The intensity of 
a sound is increased by the proximity of a sounding body, 
provided the body, or the column of air which it contains, 
can vibrate at the same rate as the sonorous body. The 
reason is that each molecule of the air is moved by the 
original source of sound, and by the body which increases 
the intensity, independently of each other. The distance 
that each molecule moves is the sum of these distances. 

361. Savart's Apparatus well illustrates the strengthening of 

sound, Fig. 131. A bell is 
made to vibrate by drawing 
a violin bow across its edge. 
A cylinder tuned in unison 
with the bell is placed at its 
side. When the open mouth 
of the cylinder is turned to- 
wards the bell, the sound is 

Fijr. i3i. much louder than when it 

is turned away, and the difference is very marked. 

£62. The Diapason, Fig. 132, illustrates the same point. 
It consists of a tuning fork, and a sound- 
ing box. When the fork is removed from 
the box, the sound is scarcely audible ; but 
when attached to the box, and the open 
end turned towards the ear, the sound is 
much louder. The reason is that the col- 
Fig. 132. umn of air in the box vibrates in the same 
time as the fork, and each source of sound acts upon the 
air, which receives the impulse of both. The sounding- 
board of a piano, or of a viol, acts in the same way. 


Section 11.— Velocity of Sound. 

363. Definition. The distance that a single sound wave 
will travel in a given time is the velocity of sound. It has 
been deterrnined experimentally, not only for air, and for 
other gases, but also for liquids and solids. As should 
be expected, it varies both with the density, and with the 
elasticity of the medium. 

364. To determine the velocity of sound experimentally, 
a sound is produced at a given instant, and the time which 
passes before it is heard at some point whose distance has 
been accurately measured is noted. This method has been 
employed in solids, liquids and gases. 

365. I. Telocity in Gases. The most accurate measure- 
ment of the velocity in air was made in 1823, by Moll 
and Van Beck, near Amsterdam. Two hills nearly eleven 
miles apart, were selected, and a cannon fired upon each. 
Light may be assumed to move that distance in an infinitely 
short time, so that the flash of the gun appears instantly. 
The length of time that elapsed before the sound was 
heard enabled the velocity to be calculated b} r dividing the 
distance by the time. These experiments gave 303 metres* 
per second, nearly, as the velocity of sound. 

366. It has since been found that these results are some- 
what varied by the density of the air. Loud sounds also 
travel at a somewhat more rapid rate than those which are 
low. It also seems probable that the rate at which sound 
travels is materially varied by the presence or absence of 
foreign substances in the air. Vapor, for example, appears 
to retard its rate. Besides, the rate is different on a calm 
day from that of a day when the air is moving rapidly. 

367. The effect of wind in retarding and accelerating 
sound is easily explained. If a sound is traveling towards 

*1093 feet. 


the wind, the molecules of air move a slightly less distance 
than they do when moving away from it. In the first 
case, their distance is the difference between their own ve- 
locity and that of the wind: in the second, the sum of the 
two velocities. So a solmd will travel quicker away from 
the wind, and also farther. 

368. Doppler's Principle. In a similar manner, if a 
person is approaching a source of sound, his ear receives a 
larger number of waves than when he is stationary, or 
moving aw^ay from it. This is known as Doppler's Prin- 
ciple. It is well illustrated by the whistle of a locomotive. 
When the engine is approaching, the whistle seems to be 
set upon a higher key than after it has passed. 

369. The velocity of sound in other gases lias been de- 
termined experimentally by using long tubes, and also by 
the note organ pipes give when filled with the gases. No 
gas shows any very great variation from the rate of motion 
in air. Yet all accord with the principle of variation of 
density an d elasticity, as sound travels faster in those which 
are more rare. 

370. II. Telocity in Liquids. Since liquids are more 
dense than gases, and are also more elastic in proportion to 
their mass, sound should travel at a proportionately greater 
velocity. This theoretical determination has been con- 
firmed by experiment. 

371. Colladon and Sturm investigated the velocity in 
water, in the year 1827. Two boats were moored at a known 
distance from each other, on Lake Geneva. Persons on 
one of them rang a bell, and the time required for the 
sound to reach the other was carefully noted. This method 
proved the rate of motion to be more than four times the 
rate in air, about 1432 metres.* 

*4708 feet. 


372. As in the case of gases, the velocity varies with 
the density of the liquid, and also with the temperature. 
Thus the rate in sea water is greater than in fresh, and a 
saturated solution of salt gives a still higher rate, while in 
ether, the sound moves slower than in water. 

373. m. Telocity in Solids. Solids are still more dense 
than liquids. They do not, howe¥er, show so great an in- 
crease in elasticity over liquids as the latter do over gases. 
Yet, as should be expected, solids transmit sounds with the 
greatest rapidity. Thus iron has been found to convey 
sounds about nine times as rapidly as air. 

374. The difference between the transmitting power of 
gases and solids was clearly shown by Biot. A bell was 
struck at the end of an iron tube 981.4 metres long,* and 
two distinct sounds were heard, one transmitted by the 
metal of the tube, and the other by the air. Sounds travel 
much further through the earth than in the air, for the 
same reason. Thus the Indians will recognize the steps of 
horses at a great distance by putting the ear to the ground. 



375. When sound waves reach the surface of a body 
whose density is different from that in which the waves 
are moving, either of three things may occur. The sound 
may be stopped by the body, either at the surface itself, 
or before it has moved very far in the body. In this case, 
the motion of the molecules is changed from a longitudinal 

*3120 feet. 


movement to motion of a different kind. This case requires 
no special consideration. It is illustrated by the effect of 
filled floors, or of partition walls, in deadening sound. 

376. When the sound is not destroyed, it may be Trans- 
mitted, or pass through; or it may be Reflected, or turned 
back from the surface. 

Section T. — IIefbactiok of Sounds. 

377. When a sound enters a medium of different density 
from that in which it has been moving, at any angle ex- 
cept a right angle, the direction in which the wave moves 
is changed. This bending takes place at the surface of the 
new medium, and is called Refraction. 

378. Sondhauss' Experiment The refraction of sound 
was proved exnernrMtilly by Sondhauss, Fig. 133. He 

constructed a large lens 
out of a collodion bal- 
loon, and filled it with 
carbonic anhydride. 
He then placed a watch 
at one focus, and its 
ticking was then dis- 
tinctly heard by the 
Fis- 133. ear placed at the other 

focus. But when the ear was removed from the focus, 
the ticking was scarcely audible. That is, the lens had 
converged the sound waves to a focus. 

379. This proof of refraction receives additional confir- 
mation by placing a balloon filled with hydrogen between 
the ear and the watch. This being of less density causes 
the sound to diverge and it becomes entirely inaudible. 

♦The Laws of Bef raction can be proved more readily in Optics. See Sec. 684. 


Section II. — Reflection of Sound. 

380. When a moving elastic body strikes the surface of 
another body, it is compressed, and it also compresses the 
body with which it comes in contact. But elasticity at 
once causes both to return to their original shape, thus 
sending the moving body back with a velocity equal to that 
with which it was originally moving, only diminished by 
the imperfection cf the elasticity. This turning back of 
a body by elasticity is called 'Reflection. 

381. Since the size of the moving body in no way af- 
fects the manner of its reflection, the laws will apply 
equally well to the molecules of a body, as air, or to the 
body as a whole. That is, sound can be reflected from the 
surface of a solid body. 

382. Laws of Reflection. Reflection is governed by two 
general laws. 

I. The angles of Incidence and Re- 
flection are equal. Let a perpendicular 
be drawn to the point of the surface 
where the body strikes, B, Fig. 134. 
AB, the path of the moving body, is 
called the line of incidence, and the 
Fig. 134. angle between that and the perpendicu- 

lar is the angle of incidence r ABD of the figure. The path 
through which the body leaves the surface is the line of 
reflection, and the angle between the perpendicular and 
that line is the angle of reflection, DBC. 

II. The angles of Incidence and Reflection are in the same 
plane perpendicular to the surface at the point where reflec- 
tion occurs. The plane ABC contains the perpendicular 
DB, and is perpendicular to the surface EF. 

383. These laws can be roughly demonstrated by experiment. 
Place a small rod perpendicular to any hard surface, as the floor, 



and throw a rubber ball at any angle, to strike at its foot. It will 

be reflected, and the eye will see 
the approximate equality of the 
angles.* Or the apparatus of Fig. 
135 may be used. It consists of a 
Fig. 135. spring which works in a tube and 

can be set to work over any one of the lines marked upon the bot- 
tom. Keleasing the spring drives a ball against the middle, and 
it is reflected back along the opposite line. 

384. Interference. When two sound waves are moving 
in the same space, the molecules of the air are subjected to 
two forces, or sets of forces, at the same time. According 
to the laws of force, each molecule must move as required 
by each sound independent of the other. With consider- 
able difference in the length of the waves from the two 
sources, no perceptible effect is produced. But when they 
are nearly or quite equal, they give rise to Interference or 
to Beats. 

385. Interference is well shown bv Fig. 136. Two bodies pro- 
ducing sound waves of the same length are made to vibrate in the 

two places, A and B, at the 
same time. Each produces 
a series of sound waves, or 
condensations, represented 
by a series of concentric cir- 
cles. But the circles whose 
centres are at A cross those 
whose centres are at B. This 
adds the condensation pro- 
duced by the body A to that 
Fig- 136. produced by the body B at 

the points x, y, z, etc., where the circles become tangent, and at 
the points a, b, c, etc., where the circles cross. Half way between 
these points, on the line AB, is a point of rarefaction, and from 
the same cause, this will be rendered twice as rare. Hence, where 
the condensations and rarefactions from the two sources of sound 
unite, the sound will be made more intense. 

386. But at the points 1, 2, 3, etc., a point of condensation from 

*Its accurate demonstration belongs to Optics. 



the source A , and one of rarefaction from B, come together. The 
motion of the molecules of air is now the difference of the two, or 
nothing. An ear then placed at such points will hear no sound. 

387. Reflection frequently produces interference. For 
let a solid, as the side of a building, be placed in any posi- 
tion, and the waves of sound will be turned back from it 
as though coming from a new source at the same distance 
behind that surface as the original source was in front. 
This gives rise to a new pet of waves which interfere with 
the first. 

388. Interference can be readily shown experi- 
mentallv by means of the Hopkins tube, Fig. 137. 
This consists of an open tube with two branches, 
and is suspended over a vibrating glass plate. The 
waves from one side interfere with those from 
the other and produce silence to an ear placed 
above the tube. 

389. Beats. If the waves of sound vary a 
little in length, those from one source will 
alternately strengthen and weaken those 
from the other source. This is called beat- 
ing, and makes the sound alternately louder 
and fainter. 

Fig. 137. 

390. Beats may be shown experimentally by placing a bit of 
wax upon one prong of a tuning fork which vibrates in unison, 
that is at the same rate, with a second.* The load causes the fork 
to vibrate a little slower, and produces beats. 

391. Echo. An echo is sound reflected from an object 
at such a distance from the source as to repeat the original 
vibrations distinctly. If the reflecting surface be in such 
a position that the sound waves strike perpendicularly, the 
echo is heard by a person at the source of sound. If the 
waves strike at an angle, the echo will be heard by a per- 
son in some other position, as required by the first law of 

*See Fig. 132, Sec. 362 



392. Multiplied Echoes. Sometimes the echo is repeated 
several times. This may be produced in several ways, and 
each is known as a multiplied echo. 

393. First. A multiplied echo may arise by reflection 
from objects at different distances. Thus Echo Lake, in 
the White Mountains of New Hampshire, repeats a sound, 
as the explosion of a cannon, four times, each report com- 
ing from a cliff across the lake. 

394. Second. Two nearly parallel sides of a valley may 
reflect the sound so that it is heard by persons located in 
different places in succession. 

Fig. 138. 

Fig. 138 shows how this is produced. If the sound be made at 
A, it will be reflected at B, a second time at C, a third time at D, 
and so on until the sound is lost by the repeated reflections. An 
observer placed in either of these lines or in others similarly situ- 
ated, would hear the sound. 

395. The Whispering Gallery renders a sound audible 
at a distance, while it remains inaudible at all intermediate 
places. This is accomplished by means of two concave 
reflectors. One person produces the sound at the focus of 
the first reflector, and it is heard by a person situated at 
the focus of the second. 

396. Fig. 139 shows the principle of- the whispering gallery. A 
person placed at F, the focus of the reflector M, produces a series 

of sound waves 
which reach the 
reflector along 
the diverging 
lines Fa, Fb, 
etc. They are 
Fig. 139. ' then reflected 

TRUMPETS. ■ 113 

according to the first law parallel. When they reach M', they are 
once more reflected, and reach the focus F', where they can be 
readily heard. In this way, two persons can carry on a conversa- 
tion inaudible to all persons between F and F'. 

397. Resonance. The sound of a person speaking is 
much varied by the room and objects in it, as the audience, 
chairs, tables, etc. When empty, the room seems to ring. 
This is called resonance, and occurs when the walls are 
not so far distant as to produce an echo. The original syl- 
lables and the reflection commingle and the reflection adds 
to the effect. 

398. Trumpets. The Speaking Trumpet and the Hear- 
ing Trumpet depend upon reflection of sound. 

399. The Speaking Trumpet, Fig. 140, consists of a 
conical tube with a mouth-piece, and a bell at the opposite 

Fig. 110. 

end. The trumpet is directed to the point to which it is 
desired to send the sound, and the waves undergo a series 
of reflections so that they are all nearly parallel when they 
issue from the mouth. The bell at the same time strength- 
ens the sound, in some way not fully explained. 

400. The Hearing Trumpet is the reverse of the above. 
It consists of a conical tube to catch the vibrations, and 
so reflect them to a point which is placed at the ear. It 
is used to enable deaf persons to hear more distinctly. 

401. Speaking Tubes leading from one room to another 
act upon the same principle. They reflect the sound from 
side to side in place of allowing it to travel in all directions. 


Division" II. — Applications. 

402. The principles of Acoustics have been applied in 
Music, both Instrumental and Vocal ; in the Representa- 
tion of Vibrations to the Eye, or Acoustic Figures ; and 
in certain instruments for Recording and Repeating the 



403. Uniformity of vibrations distinguishes a musieai 
sound from a mere noise. The vibrations of a noise are 
irregular either in the number produced in a given time, 
or in their intensity, or in both respects. Such a sound 
displeases the ear. A musical sound is produced by a defi- 
nite number of vibrations in a given time, and they main- 
tain nearly uniform intensity. 

404. Musical Sounds possess three distinct properties, 
Pitch, Intensity, and Timbre. 

405. Pitch is the quality which distinguishes between 
high and low tones, and depends upon the number of vibra- 
tions made in a given time, as one second. 

406. Intensity, as previously shown in relation to sound 
in general, depends upon the distance through which the 
body vibrates. 

407. Timbre is the peculiar quality which distinguishes 
one human voice from another, or causes the difference be- 
tween musical instruments. Helmholtz has shown by 


means of manometric flames* that it depends upon the 
production of secondary tones less prominent than those 
which are usually recognized. 

Section I. — Determination" of the Number of 

408, Savart's Toothed Wheel. The earliest determination of the 
number of vibrations which produce a given 
musical sound was made by Savart's Toothed 
Wheel, Fig. 141. It consists of a wheel 
whose rim has a known number of teeth. 
This is revolved rapidly and moves an indi- 
cator which shows the number of revolu- 
tions. A card is placed so that each tooth 
strikes it in passing. 

Fig. hi. 409. The wheel is first turned until 

the card produces the sound whose vibrations it is desired 
to determine. The index is then read, and the wheel turned 
uniformly a certain number of seconds. The index is once 
more read; and the difference of the readings gives the 
number of turns of the wheel. This, multiplied by the 
number of teeth and divided by the number of seconds, 
gives the number of single vibrations corresponding to the 

410. Limits of Perceptible Sounds. Savart determined 
the nunfber of single vibrations necessary to produce a 
continuous sound, by means of the Toothed Wheel. He 
also used a long bar to determine deep sounds. He found 
that fourteen or sixteen single vibrations must be made 
each second in order to produce a continuous sound. With 
less, the ear distinguishes a series of independent blows. 
He also found that the ear could receive as many as 4,800 
per second. When the limit is reached, silence ensues. 
But the limits are not the same for all individuals. Some 

♦See Sec. 472. 


persons can hear sounds too acute for others to recognize. 

411. The Syren. The results obtained by using the 
Toothed Wheel are approximate only. 

The Syren, Fig. 142, is a much more accurate instrument. It 
consists of a brass plate A perforated by a series of holes, set at 

Fig:. 142. 
an angle. A second plate B is perforated by the same number of 
holes so directed as to form a right angle with the direction of 
those in the plate A. The upper plate can turn, and carries an 
index to record the number of revolutions, and the whole is then 
attached to a bellows.* A series of puffs of air is thus produced 
which causes the upper plate to revolve. The air can escape only 
when the holes of the upper plate coincide with the lower, 
so that each puff corresponds to a single vibration. 

412. Weights are placed upon the bellows to increase 
the pressure and rate of revolution until the sound given 
by the Syren corresponds to the sound whose vibrations 
are to be determined. It is then allowed to revolve for 
some seconds, and the result read off from the index, and 
the vibrations determined as with Savart's Wheel. 

413. Bellows. The Bellows used to supply air to musical 

*See Section 413. 



Fig. 143. 

the pressure as great as is desired. 

414. The Timing Fork, or Diapason, Fig. 
144, is a convenient-instrument for determining 
vibrations. It is simply a fork of steel, often 
attached to a sounding-box to strengthen the 
sound. It is set to vibrating by drawing a 
violin bow across one prong, or by striking one 

instruments, Fig. 143, consists 
of a series of boards connected 
by leather. It is made air tight, 
and air is forced into it by a 
pedal through a valve. It es- 
capes through a pipe which 
carries it to any point where 
it is to be used, as to the wind 
chest at the top to drive the 
syren. Weights can be placed 
upon the top board to make 

Fig. 144. 

415, The vibrations of the prongs can frequently be seen with 
the eye, but if a needle point be attached to the fork by a bit of 

wax, and L the point 
be drawn along a 
piece of smoked 
paper, the vibra- 
tions develope a 
sinuous line ; then 
by attaching it to 
some instrument, 
as a revolving cyl- 
inder, which moves 
it uniformly, the 
Fig. 145. number of curves 

made in a given time will represent the number of vibrations. 
This is well shown by Fig. 145, in which the blackened cylinder is 
marked by the styles attached to the fork and rod. 


Section II. — The Theoky of Music. 

416. The Fundamental Note. A musical instrument is 
in tune when different notes harmonize. Two instruments 
are in tune with each other when any one note upon both 
is produced by the same number of vibrations. Since the 
tuning of instruments is thus purely arbitrary, the funda- 
mental, or. note which is used as the basis, must necessarily 
differ at different places. In determining the theory of 
music, it is placed as produced by 256 double vibrations per 
second, and called C. 

417. Normal Tuning Fork. To harmonize different 
places, a commission met at Paris in 1859, and established a 
normal tuning fork, which corresponds with C produced 
by 261 double vibrations, and most instruments now agree 
with that. 

418. Musical Scale. A sound produced by twice the 
number of vibrations per second that produce a given sound 
is called its octave. Thus the octave of C is produced by 
twice 256 double vibrations, and is c. The series of seven 
notes commencing with the fundamental C, together with 
its octave c, is called the musical scale. 

A 419. Intervals. The relation between the number of 
vibrations which produces a note and those which produce 
the next higher is called an Interval. Or, an interval is 
the quotient obtained by dividing the number of vibrations of 
any note by the number of vibrations of the next lower. 

420. The various notes of the scale are then produced 
as follows, letting m represent 256 vibrations. 

C. D. E. F. G. A. B. c. 

m. f m. f m. |m. f m. -f m. -V 5 - m. 2 m. 

421. Chords. Tones whose separate waves coincide, or 
so nearly harmonize as to please the ear, are called chords. 


If the notes are so separated that the vibrations have a 
ratio of 2:1, they may be considered the same tone. Any 
three notes whose vibrations bear the relation of 4:5:6 
please the ear. Such notes are termed a major chord. All 
whose relation is expressed by small numbers are similarly 
pleasing. If however their relation is 10: 12: 15, they differ 
very slightly, but not enough to displease, unless long con- 
tinued, or frequently recurring. Such notes constitute the 
minor chord. 

422. Music is a variation of the order and succession of 
the notes which will produce the chords. The notes which 
will give the major chord are : 

C:E:G=4:5:6, called tonic. 
G:B:d=4:5:6, called dominant. 
F: A:c=4:5:6, called sub-dominant. 

423. Tones and Semitones. Comparing the intervals, 
three fractions are found, f , ^ and j-f , as follows : 

CtoD DtoE EtoF FtoG GtoA AtoB Btoc 

9 10 16 9 10 9 1 6. 

8 9 15 8 ~9~ 8 T5 

The first two are tones, the third a semitone. 

424. For convenience in music, a semitone is introduced 
between each pair of notes where the interval is a tone. 
This is done by raising a note a semitone, that is by mul- 
tiplying it by H, and is called sharping the note. 

425. If in place of sharping one note, the note above is 
lowered by a semitone, it is said to be flatted. In this 
case the note is multiplied by f|. 

426. Tempering. Because the intervals between the 
sharp of one note and the flat of the next vary a little in 
length, the transposition of the scale would be impossible 
without a separate set of musical instruments to play each 
transposition. This is clearly impossible. 


4:27. To remedy this defect, the entire number of vibra- 
tions between C and c is divided into eleven equal spaces, 
each interval being l2 V 2- This is called tempering, and is 
applied in all common musical instruments, as the piano 
or organ. 

Section III. — Musical Instruments. 

428. Musical Instruments produce musical tones in two 
ways, by the vibrations of tightly stretched cords, and by 
causing a column of air enclosed in a tube or pipe to vibrate. 
In the first, the vibrations are transverse, that is, the string 
moves from side to side : in the second, the molecules of 
air move in the direction of the length of the pipe, so pro- 
ducing an alternate condensation and rarefaction. The 
former are stringed instruments, as the piano and viol; the 
latter are wind instruments, as the trumpet and organ. 

429. The use of a sounding board or box, to vibrate in 
unison with the sound produced, increases the effect, both 
with stringed instruments, and wind instruments. 

430. Laws ol the Titrations of Stretched Cords. The Sonometer 
or Monocord, Fig. 146, is used to determine these laws. It con- 
sists of a string stretched 
above a thin sounding 
box. The tension can be 
varied by changing the 
weights attached to the 
end which passes over 

Fig. 146. the pulley. A movable 

bridge allows the length of the vibrating portion to be varied. 
It is usually vibrated by a violin bow. 

431. Experimental Determination. I. Lengths. Let 

the cord be vibrated without the movable bridge. It now 
gives a certain note, usually the fundamental, of 256 vibra- 
tions. Then by inserting the bridge -^ from the end, f of 
the cord is made to vibrate ; the tone is now D. Using |, 


the tone is E. This may be continued with each note 
of the entire scale.* The length of the vibrating cord is 
thus the reciprocal of the number of vibrations pro- 
duced. Hence the Law: The Number of Vibrations varies 
inversely as the Length. 

4:32. II. Diameters. Attach a second cord to the 
Sonometer, whose diameter is two-thirds of the first, and 
cause both to vibrate. They give the chord of the fifth. 
By placing the movable bridge at two-thirds the length of 
the larger cord, they can be brought into unison. Hence, 
The Number of Vibrations varies inversely as the Diameter 
of the Cord. 

433. III. Tension. If two cords of the same material and 
diameter be attached to the Sonometer, and be stretched 
by weights whose proportion is 4:9, they will give the cord 
of the fifth. They are brought into unison by placing the 
bridge at two-thirds the length of the cord stretched by 
the smaller weight. But the lengths, or the number of 
vibrations now produced, are proportionate to the square 
root of the weights, or as 2:3. Hence the Law: The 
Number of Vibrations varies as the Square Root of the Ten- 

434. IT. Density. When strings of the same diameter, 
and stretched by equal weights, but of different materials, 
are used, they give different notes. They may be brought 
into unison by placing the bridge under the one which 
gives the lower tone. Comparing their lengths with the 
Table of Specific Gravity,! their lengths are seen to be 
proportional to the square root of their specific gravities. 
That is, The Number of Vibrations varies inversely as the 
Square Root of the Density. 

435. Nodes and Loops. If a single cord be stretched 

♦See Sec. 423. 

tSee Table V at end of the volume. 


upon the Sonometer, and the bridge be placed at a distance 
which is an aliquot part of the length, as one-third, the 
entire string vibrates producing a single tone. As can be 
readily seen, where it rests upon the bridge, there is no 

436. The portion beyond the bridge must be divided in 
the same proportion, or two tones would be produced 
That is, if the proportion is one-third, there are two points, 
or nodes, where there is no vibration. 

Fig. U7. 

437. The cord in adjacent segments is moving in oppo- 
site directions. That is, if it moves downward in the mid- 
dle, it moves upward in the ends, and conversely. Fig. 147. 
Ab represents a vibrating string: as the part 3 ascends, 9 
descends, and so on. 

438. The existence of these nodes and also of the loops 
between them, is clearly shown by bending pieces of paper 
to form riders, and applying them to different parts of the 
stretched cord. Those upon the nodes remain : those upon 
the loops are thrown off. 

439. Yery often the cords of a stringed instrument vi- 
brate as a whole, and at the same time in nodes. This 
produces more than one tone by the vibration, and gives 
rise to harmonics. Short cords do this much less frequently 
than those which are longer, and these subordinate tones 
combine with the vibrations of the sounding board to pro- 


duce the difference of timbre noticed in different instru- 

440. The stringed instruments now used are made in 
accordance with these laws. They are of two kinds, those 
in which the length of the string is invariable, as the piano: 
and those in which it can be varied, as the viol. 

441. The Piano consists of a series of metal cords 
stretched over a sounding board. The difference in the 
sound of different instruments is caused by varying the 
materials of the sounding board. The cords vary both in 
length and in diameter, to produce the different notes. 
The sound produced by each string is invariable. Hence 
this instrument is tempered. 

442. The Yiol consists of a series of strings, usually of 
some animal membrane, stretched upon a sounding box. 
The different sounds are produced by pressing the finger 
upon the cords at different points, which changes the length 
and also the tension. So the same cord may give any re- 
quired tone, and the instrument requires no tempering. 

Other stringed instruments, as the harp or the guitar, 
are made similar to one of the above. 

443. The difference of tone produced by different stringed 
instruments arises from the vibration of the sounding box 
in segments. This gives subordinate tones at the same 
time as the principal. The manner in which these nodes 
and loops occur will be shown under Acoustic Figures.* 

444. Wind Instruments are of two kinds differing in 
the manner in which the air is set to vibrating: mouth 
instruments and reed instruments. 

^See Section 4*1. 



115. In Mouth Instruments, the 

air enters by a small opening, P, Fig. 
118, and escapes by a beveled passage 
i, so striking against a thin upper 
lip a. This produces a series of shocks 
and sets the air contained in the pipe 
into vibration. A whistle is made in 
this way. 

The tone of the instrument is de- 
termined by the length of the col- 
umn of contained air. Hence the 
different notes can be produced by 
varying its length, either by holes 
closed by the fingers, as in the flute, 
or by holes opened by keys as in the 
clarionet, or by both arrangements. 
In many instruments, the checks and 
the air contained within the mouth 
are made to act as a mouth-piece. 

148 - Most band instruments, as the horn, 

kind. The trumpet acts similarly. 

116. A reed consists of a tongue of metal or wood V, 

Fig. 119. A current of air en- 
tering downwards, towards 
the reed, carries the reed 
forward and closes the aper- 
ture. The elasticity of the 

Fig. 149. 

tongue quickly carries it back, and opens the aperture again, 
thus causing the air to vibrate. Reeds are of two kinds, 
depending upon the manner in which the vibrating tongue 
operates : Free Reeds and Beating Reeds. 

117. Free Reeds vibrate back and forth between the 
sides of the aperture, and the number of vibrations is de- 
termined bv the length of the tongue. They are often 



used to cause the column of air in an organ pipe 
T, Fig. 150, to vibrate. Such a reed is placed 
in a box K, and its length is determined by a 
small wire. 

4:4:8 ' Beating Reeds are so constructed that 
the tongue strikes the edges of the opening. 
This alternately allows the air to pass, and cuts 
it off. Such a reed is used in the Clarionet. 

449. Organ Pipes give tones determined by 
the relation of their length to their internal 
area. The length of an open pipe must how- 
ever be double that of a closed pipe to give the 
same sound, because the sound pulse in a 
closed pipe must travel twice the length of the 
pipe: in an open pipe, once. 

™ 450. The pupil can readily construct a reed 

Fig. 150. an( j pjp Q by cutting a tongue near the joint of 
a large straw, and then blowing into the straw. 

451. Organ pipes have nodes and loops, similar to those 
of strings. The particles of air at the node do not change 
their position, but there is at that point an alternate con- 
densation and rarefaction. At 
the loop, the density of the air 
does not vary, but the particles 
move back and forth through 
a distance proportionate to the 
number of vibrations produced 
in each second. 

452. The Nodes and Loops of an 

organ pipe can be readily shown 

by pipes having two holes on one 

side. Fig. 151. One of these is 

Fi ~ m over a node, and the other over a 


loop. A thin membrane is stretched over the hole, and a gas pipe is 
attached, with a jet, as shown in the figure, fastened to the stand. 

453. When the air at the node is condensed, it presses 
the membrane forward, closes the opening, and puts out 
the light. The jets at the loops continue burning. A re- 
volving mirror is often placed at the side, to render the 
changes of the flames made by the burning jets visible. 



454. The figures produced by the nodes and loops of vi- 
brating bodies are called Acoustic Figures. They may be 
rendered visible in two ways, as follows: 

455. I. Sand is placed upon the vibrating body, and is 
driven from the loops and accumulates upon the nodes. 
This method is applicable to vibrating plates, and other 
flat bodies, as stretched membranes. 

456. II. Some appliance may be used which causes the 
vibrating body to affect light. This may be either by re- 
fleeting the light from a mirror, or by variation of the 
flame which is the source of the light. 

Section" I. — Vibrations of Plates and Membranes. 

457. The tone produced by a vibrating plate is governed 
by laws which determine the vibrating parts, and the in- 
tervening nodes. These laws depend upon the size and 
thickness of the plate; its shape; and the points by which 
it is held. 

458. The Nodal Lines may be rendered visible by strew- 



ing fine sand upon the plate. Since the sand soon collects 
upon these lines it leaves the vibrating parts uncovered. 

459. To determine the figures experi- 
mentally, a brass or glass plate is first 
clamped by the centre.* Fig. 152. It is 
then vibrated by drawing a violin bow- 
across the edge. The point by which it 
is held cannot vibrate: hence all nodal 
Fig. 152. lines pass through that point. Or the 

same effects may be produced cheaply by using common window 
panes, as follows : A pane of glass is supported by its middle 
point upon a small block of soft rubber. A long glass tube is then 
fastened to its upper surface by wax or paraffin . This tube is then 
held by the thumb and finger of the left hand, and rubbed by the 
thumb and forefinger of the right hand, first moistened with a 
little water. This produces intense vibration. 

460. So long as the plate gives the same tone, the sys- 
tem of nodal lines remains constant. But by touching 
any point in the edge with the finger, that point is made a 
node, a new sound is produced, and a new system of nodal 
lines developed. 

461. By clamping 
the plate at other points 
than the centre, new 
tones and nodal lines 
can be produced. The 
tones will be pure 
whenever the clamping 
point is an aliquot part 
of the distance across 
Ffc. 153. the plate. Fig. 153 

shows some of the forms given by the nodal lines. 

462. Chladni's Law. Chladni determined by experi- 
ment that the following law governs the figures produced 

*A brass plate is usually made circular: a glass plate, square. 


with different vibrating plates. In plates of the same ma- 
terial and dimensions, the number of vibrations per second 
varies directly as the thickness, and inversely as the area. 

463. Gongs and cymbals are practical applications of 
vibrating plates. 

464. Membranes can only vibrate when tightly stretch- 
ed. They then vibrate in segments, much as plates vibrate 

and the segments can be rendered 
visible by sand. Fig. 154 shows 
the segments of a tightly stretched 
rig. 154. membrane thrown into vibration 

by proximity to a sounding body. 

465. Membranes are applied in the drum and tamborine, 
and are made to vibrate by blows. In the drum, the vi- 
bration is strengthened by the enclosed column of air. 

466. All stretched membranes, and indeed all surfaces, 
are made to vibrate by any sounding body, the vibrations 
being transmitted by -the intervening air. Thus if a violin 
be sounded near a piano, the sounding board of the piano 
will vibrate in unison with the violin. 

Section II. — Optical Representation of Vibrations. 

467. Lissajous' Figures. A very light reflector, m, 
Fig. 155, is attached to one prong of a tuning fork, and 
a balancing weight, n, to the other. A lamp surrounded 
by an iron chimney which has a small hole in it, is placed 
some yards distant, so as to send a single beam of light 
upon the tuning fork, and the eye is placed so as to see the 
reflected light. By reflecting this beam a second time 
through a lens* it may be projected upon a screen. 

*See Section 701. 



Fig. 155. 

468. Image Produced by a Single Vibrating Body. 

When the tuning fork is still, the reflection is a circular 
spot. When it vibrates, the spot becomes a line. Turning 
the fork around changes the line into a series of waves. 

469. Combination of two Vibrations. If two forks 
which vibrate at the same rate are placed parallel, the line 
is lengthened. If they vibrate at different rates, the line 
is alternately lengthened and shortened. Thus the beats 
which the ear distinguishes are made plain to the eye. 

470. If two forks are placed at right angles, one pro- 
duces an image which is horizontal, and the other a vertical 

image. Wlien both vibrate, 
these two images combine. 
If they are very nearly in 
unison, the changes of Fig. 
156 follow each other in or- 

x 4 

Fig. 156. der. If they differ by an oc- 

N. P. 9. 







tave, they produce a figure eight, as shown in Figure 156. 

471. These experiments may be continued with forks 

varying in any pro- 
portion, and each 
combination will 
give its appropriate 
figure. The fol- 
lowing illustration, 
Figure 157, shows 
some of these, the 
fractions under 
each par b of the lig- 
. fig, 157 . ure denoting the 

proportionate rates at which the two forks vibrate. 

472. Koenig's Manometric Flames. Koenig employed 
a gas iet of the form shown in Fig. 158. A very elastic 
rubber diaphragm is stretched 
across a large chamber. A tube 
conveys the vibrations of air to 
one side of the chamber. The 
other is supplied with burning 
gas by a tube and stop-cock, 
and the gas passes from the 
chamber to a burner. 

473. A square revolving mir- 
ror is placed in front of the gas 
flames. When no sound is made the image of the flame 
in the mirror is elongated, and forms a band with parallel 
sides. Koenig used a series of these jets and flames at- 
tached to hollow cylinders capable of being lengthened and 
shortened, to determine the cause of timbre. He found 
that when a pure tone, such as is made by a tuning fork, 
is produced, only a single flame is affected, the one whose 
resonance cylinder corresponds to the fork. When any 



musical instrument gives the same note, this flame and 
others also are caused to move. This shows that the dif- 
ference of tone of different instruments, or timbre, results 
from subordinate tones accompanying the principal, and 
Helmholtz has succeeded in confirming this analysis of 
sounds by putting these tones together, and producing the 

474. If a sound be 
conducted to the cham- 
ber, the image is cut up 
into a series of tongues, 
one of which corres- 
ponds to each vibra- 
tion. The images can 
be photographed. Fig. 
159 shows a note and 
its octave. When sev- 
eral tones are combined 
the flame vibrates with 
each, and this makes a 

Fig. 159. 

series of long tongues with shorter ones between them. 
The number of long tongues gives the number of vibra- 
tions of the lowest note; the shorter ones, the number of 

the higher notes. 



475. Two remarkable instruments have been constructed 
which employ vibrating membranes, or diaphragms, the 
Telephone, and the Phonograph. 



Section I. — The Telephone. 

476, The action of the telephone depends upon the va- 
riation of the strength of a magnet by placing an arma- 
ture near it, and by the induction of an electric current by 
the magnet.* 

477. The Telephone, Fig. 160, consists of a small bar magnet 

surrounded by a 
coil of insulated 
copper wire. A thin 
elastic plate of iron 
is placed in front of 
the magnet, but not 
touching it. The 
copper wire passes 
out of the case, and 
by means of the 
binding screws at 
the bottom, and 
the line wire forms 
an electric circuit 
with a second tele- 
phone. The mouth- 
piece of one is used 
by the speaker, and 
the other is placed 

. Fig. 160. at tlie ear of the 

hearer. While the right of Fig. 160 shows a plane section of a tel- 
ephone to show its various parts, the left shows the same instru- 
ment in its case ready for use. 

478. The telephone acts as follows; the waves of sound 
move the diaphragm back and forth. Each motion of the 
diaphragm causes a current of electricity to pass through 
the wire, and so moves the diaphragm of the receiving 
telephone to correspond with its own movements. This 
diaphragm sets up a second set of sound pulsations. 

The distance between the telephones is limited by the 
resistance of the intervening wire. 

*See Electricity, Section 03G. 


479, The Photophone. The force which carries the 
movements of the sound and reproduces them at a distance 
in the telephone is electricity. The later instrument, the 
Photophone, uses light for the same purpose. Waves of 
sound set a diaphragm into vibration, as in the telephone, 
but this diaphragm is really a very light mirror. A beam 
of light is alternately increased and diminished in intensity 
by this mirror, and this light allowed to strike a distant 
diaphragm there reproduces the vibrations, either directly 
or through the medium of increasing and diminishing the 
electrical power of a piece of silenium, which acts upon a 

Section IT. — The Phonograph. 

480. The Phonograph. Fig. 162, consists of a grooved 
iron cylinder which can be turned by a crank. A screw is 

Fig. 162. 

attached to one end, the distance of whose threads is the 
same as the distance of the grooves apart. The cylinder 
is covered with tin foil. A thin vibrating diaphragm which 
carries a very fine needle point is so placed that the point 
at rest just touches the tinfoil. 

481. If now sounds be made in front of the diaphragm, 
and the cylinder turned, the point must move back and 
forth with the air. Each pulsation is then recorded by a 
depression in the tinfoil. 


482. By causing the style to pass a second time over the 
tinfoil, the sounds will be repeated in a new series of pul- 
sations made by the diaphragm moved back and forth by 
the attached style. 


1. Section 365. A stone is dropped into a pit, and the 
sound is heard two seconds after it is seen to strike the 
bottom. Required the depth of the pit. 

2. A man counted 36 beats of his pulse, which makes 70 
beats per minute, between a flash of lightning and the 
thunder. Required the distance of the cloud. 

3. Section 391. An echo repeats four syllables, each of 
which it requires a fourth of a second to pronounce, and the 
echo is heard one-fourth of a second after the last is ut- 
tered. How far distant is the object which produces the 
reflection ? 

4. Section 373. A man at a distance strikes a blow upon 
some ice, and two sounds are heard two and a half seconds 
apart, one transmitted by the earth and the other by the 
air. How many metres distant is the man? 

5. Section 365. The report of a cannon is heard by a 
man twenty miles distant. How long is it after the can- 
non is fired? 

6. Section 431. Two strings of the same diameter and 
stretched by the same weight give notes distant by an oc- 
tave. How do their lengths compare ? 

7. The lower string of problem 6 gives C. What must 
be the length of the other to make the chord of a fifth ? 
How many times will it vibrate each second? 

8. Section 445. A closed organ pipe gives the note D 


and an open pipe near by makes a chord of the fifth with 
the pipe. Required its comparative length. 

9. How many vibrations do each of the above pipes make 
each second ? 

Pakt II. — Heat. 

483. Definition. Heat in common language usually 
means the effect produced upon the senses by a heated 
body. In Physics, Heat is used for the cause of this sen- 

484. Careful experiments indicate that the molecules of 
all bodies are always moving. When the movements of 
the molecules of a body are at right angles to the direction 
in which the force advances, that is a transversal vibration 
of a certain definite length, the motion is called heat.* 

485. Temperature. The effect produced upon our senses 
by a heated body is called temperature. When a body 
whose molecules move further, or more rapidly than those 
of the human body, is touched by the hand, it increases 
the motion of the molecules of the hand, and is called hot. 
But if it diminishes the motion of the molecules of the 
hand, the body is called cold. Hence our senses only give 
us difference of temperature. 

486. Hot and Cold, are then relative terms, and we may 
pronounce the same body hot or cold according to circum- 
stances. Thus if one hand be placed in melting ice, and 
the other in water as hot as can be borne, upon removing 
them and plunging both into water of the temperature of 
the blood, it will feel hot to one hand and cold to the other. 

Heat, then, is only known from its effects. 

♦Heat and Light seem to be identical, differing only in the length of the 





487. The only known effect of heat is to increase the 
rate and distance of the motion of the molecules of a body. 
But the difference in the states of matter causes apparent 
differences in the effects. Hence expansion produces Fu- 
sion, Vaporization, and Spheroidal Condition. 

Section I. — Expa^sioi*. 

488. All bodies expand when heated, and the rate of 
expansion varies with the state, as well as the material, 
gases expanding the most rapidly, and solids the slowest. 

489. Expansion of Solids may be considered in one 
direction, or Linear; in two, or Superficial; or in three, or 

490. Linear Expansion may be proved by the Pyrome- 
ter, Fig. 163. This consists of a metal rod one end of 

which is fastened, while 
the other moves freely, 
and turns an index. The 
bar is adjusted so that 
the index points to zero. 
A lighted spirit lamp is 
Fig, 163. then placed under the 

rod, and the expansion moves the index. 



491. Superficial Expansion can be readily- 
seen by using a piece of sheet iron with a 
circular hole in it that a second piece will 
just pass through when both are cold. After 
heating the small piece, its expansion pre- 
vents it from passing through. 

492. Cubical Expansion may be proved 

by Gravesend's Ring, Fig. 161. A ring of 
brass allows a ball to pass through when 
cold. When heated, it will not pass through. 

Fig. 164. 

493. Expansion of Liquids. The apparatus of 
Fig. 163 shows the cubical expansion of liquids, 
and at the same time shows that they expand 
more rapidly than solids. A flask is fitted with a 
cork and glass tube. It is then filled with some 
liquid, as water,* and the cork pressed in so as to 
cause the liquid to rise a short distance in the 
tube. When the flask is heated, both glass and 
water expand. But the water rises in the tube, 
showing that the liquid expands the more rapidly. 
Fig. 165. and its rate measures the difference. 

494. The Cubical Expansion of Gases can 

be shown by a bulb of glass upon the end 
of a long stem, Fig. 166. It is called an air 
thermometer. Inverting the tube in a vessel 
of water, and bringing a source of heat near 
the bulb, the air expands and escapes in a 
stream of bubbles. 

495. Coefficient of Expansion. The 

amount which a body whose dimensions are Fig - 166 - 
unity expands in passing from zero to one degree is called 

*If it be colored by a little aniline red, it can be better seen. 

138 HEAT. 

the Coefficient of Expansion. If the heating continues, the 
body expands at nearly the same rate until it approaches 
the melting point. Hence if a be the expansion in length 
for one degree, or its Coefficient of Linear Expansion, (a 
quantity determined by experiment for every substance,) 
for t° it will expand t times as much, or at, and its length 
after expansion will be 1+at. 

496. The Superficial Expansion is found by squaring 
the length, or is l + 2at+a 2 t 2 . But a is very small for all 
known substances, so that a 2 becomes inappreciable, and 
the term containing it may be neglected. Hence the Coef- 
ficient of Supercificial Expansion is twice that of Linear. 

497. So also, the Coefficient of Cubical Expansion is 

found by cubing the length, that is, l + 3at + 3a 2 t 2 + t 3 . 
For a similar reason as before, all the terms after the sec- 
ond are inappreciable. Hence the Coefficient of Cubic 
Expansion is three times that of Linear. The expansion of 
solids can be measured in all directions : only the last 
formula applies to liquids and gases. 

The relation of these formulae shows that with solids 
the linear expansion only needs to be measured. This is 
accomplished with accuracy by using three rods of the 
material whose expansion is required. Small rods are at- 
tached to these, with fine wires, so that they can be placed 
exactly in a straight line. Two of these rods are then 
placed in ice, and the third is placed in some hot liquid 
whose temperature is known. This causes the middle rod 
to expand, and its expansion can be measured by the 
amount the wire is moved from the line. This divided by 
the temperature gives a. 

498. Temperature. The difference in the rate of expan- 
sion between solids and liquids is employed to measure 
temperature. Instruments for doing this are called ther- 



mometers. They are made of glass, and are usually filled 
with mercury, but sometimes with alcohol. 

499. Making Thermometers. The operation of making 
a thermometer consists of three distinct steps : The Cali- 
bration of the Tube : Filling with Mercury : and Graduation. 

500. Calibration of the Tube. The dimensions of the 
tube must be uniform throughout its entire length, else 
equal expansion of the mercury will be indicated by unequal 
variations on the stem. To determine that they are so, a 
small amount of mercury is placed in the tube and moved 
to different parts of the tube. Its length is carefully 
measured, and should remain constant in all positions. If 
the length of the mercury varies, the tube is valueless. 

501. Filling the Tube. A bulb, D, Fig 
167, is next blown upon one end of the 
tube, and the other is enlarged to form a 
small funnel. As the tube is too small 
to allow mercury to flow freely through 
it, since capillary repulsion prevents, the 
pressure of the atmosphere is used to force 
it to enter. A small amount of pure mer- 
cury is placed in the funnel, and the bulb 
heated. This expands the air in the bulb 
and forces some of it out. The bulb is 
next cooled, when the pressure of the air 
upon the mercury in the funnel causes a 
small amount to pass into the bulb. This 
is then boiled, so that mercury vapor expels 
all the air and fills the bulb and tube. The 
bulb is once more cooled, and the atmos- 
pheric pressure fills bulb and tube with 
mercury. The whole instrument is now 
heated to a temperature higher than that 
which the thermometer is intended to indicate, and the 
stem sealed by melting the glass in the blowpipe flame. 



502. Graduation. The fixed points, boiling find freezing, 
are first determined. The boiling point is found by placing 

the thermometer in a brass vessel 
of the form of Fig. 168, that the 
bulb and the stem nearly to the 
top may be surrounded by steam. 
The lower part, M, is placed upon 
a furnace, and the steam ascends 
in the part A, and descends in the 
part B. D allows the steam, and 
any condensed water to escape. 
A manometer* at E shows that 
the pressure in the vessel remains 
the same as that of the air. When 
the mercury ceases to rise in the 
stem, the point at which it stops 
is marked boiling point. 

Fig. 1G8. 


The thermometer is next placed 
in a vessel containing melting 
A hole in the bottom allows any water formed to 
escape. When the mercury has come to rest, the point is 
marked freezing point. The space between is then divided 
into equal parts, and the graduation continued above and 
below the fixed points. 

R. C. I F. 

503. Scales of Thermometers. Three distinct scales are 
in common use, Fahrenheit's, Centigrade, and 
Reaumur's. The first is commonly used in 
this country except for scientific work, where 
the second is used. Fahrenheit's scale marks 
the freezing point 32°, and the boiling point 

i212°: Centigrade marks these points 0° and 
100°: Reaumur's 0° and 80°. Fig. 169. 

Fig. 169. 

504. Relation of the Scales. Since the same 

*See Section 327. 



space is divided into a different number of spaces, the length 
of each space, or of a degree differs in the several scales. 
The proportion between them is as follows : 

F:C:R=180 o :100°:80° 
Reduced this becomes F:C:R=9:5:4. 
This proportion furnishes the means of changing from one 
scale to another, only recollecting that if the Fahrenheit 
scale is required, 32° must be added to the result, because 
of the difference of zero point: and if that scale be given, 
32° must first be subtracted. 

505. Limits to the Thermometer. Since mercury freezes 
at 40°C, it cannot be used to indicate temperature below 
that point. For this purpose, a thermometer filled with 
alcohol is employed. 

Mercury boils at 350°C. Hence a pyrometer is used to 
measure temperatures above that point.* 

506. Applications of Expansion. Two applications of 
expansion of solids and liquids deserve special notice: the 
Compensating Pendulum, and the use of Tie Rods. 

507. The Compensating Pendulum. Two 

forms of Compensating Pendulum are in com- 
mon use, the Gridiron Pendulum, and the 
Mercurial Pendulum. 

508. The Gridiron Pendulum, Fig. 170, 
depends upon the unequal expansion of dif- 
ferent metals for equal changes of tempera- 
tures ; e. g., steel and copper. The pendulum 
consists of a series of parallel bars, the out- 
side ones of steel attached at .the top, which 
expand downward and lower the bob. The 
next bars, of copper or brass, are attached at 
the bottom, and the bob is suspended from 
their top. They then expand upward, and 

Fig. i7o. raise the bob. When rightly proportioned, 


*3ee Sec. 490. 

142 HEAT. 

they raise it the same distance that the steel rods lower 
their own point of attachment, so that the centre of gravity 
of the bob remains at a constant distance from the point 
of support, and the times of oscillation are equal. 

509. The Mercurial Pendulum, Fig. 171, consists of a 
stirrup of steel, &, suspended by a steel rod, a, car- 
rying a glass vessel, c, filled with mercury. As 
the expansion of the steel rod lowers the centre 
of gravity of the mercury, the upward expansion 
of the mercury itself raises it an equal amount. 
This pendulum is usually considered more accurate 
than the former. 

510. Compensating Balance Wheels for watches 
are made upon the same principle. They consist 
of pieces of two different metals, the expansion of 
one of which enlarges the wheel, while the expan- 
sion of the other contracts its diameter. Its oscil- 
lations thus remain constant. 

rig. ni. 5i l The Force of Expansion and Contraction 

is also employed in tie rods, used to hold parts of buildings 
together. They must then be so constructed as to allow 
free motion from expansion. This is usually effected by 
making all bolt holes elliptical. 

512. Buildings that have started apart are sometimes 
drawn together by the same force. Tie rods are placed 
across the building, and the nuts on the end screwed up as 
tightly as possible. The rods are then heated, and the expan- 
sion loosens the nuts, which are once more tightened. 
When the rods again cool, the sides of the building are 
drawn towards each other with the whole force of tenacity, 
and brought into their proper position. 

513. In a similar way, the tires of wheels are heated 
before they are placed upon the wheels. Their contraction 


then binds tne parts firmly together. Iron barrel hoops 
are sometimes put on hot for the same reason. 

Section II. — Fusion and Solidification. 

514. Fusion is the change from a solid to a liquid. 
When the temperature reaches a certain point, differing 
with the substance, all apparent expansion ceases, and the 
effect of further heating is to change the state. Formerly, 
certain bodies were considered refractory, that is infusible, 
but all except carbon have been melted, and that has been 
rendered flexible. 

515. Laws. Experiments upon different substances have 
shown that fusion is governed by two laws: 

I. Every substance melts at a certain invariable tempera- 

II. The temperature remains constant during fusion. 

Thus, if a mass of ice be heated to 0°, it begins to melt. 
Continue the heating, and the ice continues to melt, but 
the water produced remains at 0° until all the ice is fused. 

These laws apply only when the pressure remains con- 
stant, and the explanation of the second is that a certain 
amount of heat becomes latent, that is, is used to move the 
molecules apart and change the state. 

516. "Vitreous Fusion. Some substances, like glass, pass 
from a solid to a liquid gradually, through an intermediate 
waxy state. They can then be bent, or moulded into any 
desired form. This is called Vitreous Fusion. 

517. Effect of Change of Pressure. If a body expands 
when melting, increase of pressure raises the melting point. 
Ordinarily, expansion occurs against the pressure of the 
air. Increase of pressure above one atmosphere increases 
the work done, so that more force is required to overcome 
the pressure and the melting point raised. But if the body 

144 HEAT. 

contracts when melting, as is the case with water, the con- 
trary effect is produced, and the melting point is lowered; 
though with water it is only a fraction of a degree for each 

518. Alloys are -mixtures of two or more metals, and 
they have the curious property of melting at a lower tem- 
perature than either of their constituents. Thus Rose's 
fusible metal, an alloy of four parts Bismuth, one part 
Lead, and one of Tin, melts at 94°. Alloys are used to di- 
minish the heat arising from friction, as in the bearings of 
the crank shaft of the mowing machine, and for soldering. 

519. Fluxes are substances which added to a metal, or 
an ore, reduce the melting point. They are used in sepa- 
rating ores from their impurities, and in welding. Borax 
is one of the best for the latter purpose. 

520. Solution is dissolving a solid in a liquid. Since it 
involves change of state, some heat must be rendered latent, 
and the temparature falls. The most common solvent is 
pure water, which dissolves most salts, gums, and sugars. 

521. In some cases of solution, the temperature is raised, 
as when caustic potash is dissolved in water. This arises 
either from contraction of volume, the solution occupying 
less space than the original substances; or from a chemical 
union of the two substances. 

522. Solidification is the opposite of fusion, and is gov- 
erned by the same laws. It takes place at the same tem- 
perature as that at which the body fuses, and all the heat 
absorbed in fusion is given out in solidification 

523. The presence of foreign matters in a liquid, so 
forming a solution, changes the point of solidification, 
usually lowering it. Thus sea water, a solution of common 



salt, with a few other salts in minute quantities, freezes at 
a much lower temperature than fresh water. 

524. Crystallization. Most salts, and many other sub- 
stances, in solidifying, assume certain definite forms. 
are called crystals, and the process, crystallization. Why 
they do this is not known. The molecular attraction seems 
to be greater in certain directions than in others, and these 
directions are called the axes of the costal. These axes 
may be represented by straight lines, and they meet at 
d finite angles, which are invariable fur each substance. 
Thus water crystallizes around three -axes which meet at 
angles of 60°. Some of the forms of snow-flakes, which 
well illustrate the principle, are shown in Fig. 172. Their 
beauty is remarkable. 

Fig. 172. 

525. The process of crystallization from a solution may 
be readily illustrated by making a saturated hot solution 
of alum, or of sugar, and suspending a thread in it. As 
the solution cools, the solid crystallizes on the thread. 

N. P. 10. 

146 HEAT. 

Rock candy is thus made from sugar, and is perfectly pure. 
In fact, in all cases of crystallization, the impurities present 
remain in the liquid where the crystals are formed, called 
the mother liquid. 

526. Change of Volume. Closely connected with crys- 
tallization is the change of volume of substances when 
passing to the solid state. Most substances contract when 
solidifying. Thus tallow and the fatty acids contract con- 
siderably : and also many metals. 

527. Maximum Density of Water. Water, and some 
metals, like iron and bismuth, expand in solidifying. This 
causes ice to float, since its specific gravity is only .92. Such 
substances are more dense at some temperature above the 
point of solidification than at that temperature. 

528. The temperature of the greatest density of water 
is shown by means of the apparatus of Fig. 
173. A glass cylinder having a thermometer 
fixed in the side at the top and another near 
the bottom, is filled with water of a given 
temperature, e. g. 15°. Around the middle 
of the cylinder is a copper vessel which is 
filled with pounded ice. As the ice melts, 
the water is cooled, and that which is of the 
greatest density sinks to the bottom. After 
sufficient time has passed, the thermometer 
at the top indicates 0°, while that at the bot- 

torn indicates 4°. So then water is the densest 
at 4°, and expands both ways from that temperature. It 
seems probable that this expansion in solidifying is related 
to the form of the crystals of the substance. 

529. The expansion of water when freezing often bursts 
water pipes and vessels in which it is contained. The great 
force exerted was well shown by the experiments of Maj. 


Williams in Canada. He filled a thirteen -inch bomb shell 
with water, drove an iron plug weighing three pounds 
into the hole, and then exposed it to intense cold. After 
some time, the plug was driven out with sufficient force to 
carry it four hundred and fifteen feet. At the same time, a 
cylinder of ice eight inches long was forced out. In a 
second experiment, the shell burst. Probably the water 
all remained as a liquid until the moment of bursting, and 
then froze instantly. 

530. If the liquid remains perfectly quiet, it can be 
reduced far below the freezing point before it solidifies. 
Thus, in a still room, water can be cooled to about — 15°, 
and yet remain a liquid. But if it be agitated, the tem- 
perature at once rises to 0°, and the whole mass solidifies. 
So some salts will not crystallize from a solution until a 
solid is placed in the solution. Then crystallization com- 
mences at the solid, and goes on very rapidly. 

531. Freezing Mixtures. The absorption of heat in the 
cnange of state of a .body when passing from a solid to a liq- 
uid is used in freezing mixtures. These consist of substances 
Avhich have strong attraction for each other, one or all of 
which must be solid. They are most effective when the 
result of their union solidifies at a much lower tempera- 
ture than either of its constituents. 

532. One of the most common freezing mixtures con- 
sists of two parts pounded ice, or snow, and one part com- 
mon salt. This quickly liquifies and reduces the tempera- 
ture to — 18°. This mixture is employed in freezing ice 

Section III. — Vaporization. 

533. When a liquid is heated beyond a certain point, 
which varies with the liquid, the motion of the molecules 
overcomes the cohesion, and the body becomes a gas. The 

148 HEAT. 

distance to which the molecules move, and the rate of 
motion are greatly increased. This change is Vaporization. 
Thus water expands about seventeen hundred times in 
becoming a gas. 

534. Vaporization takes place in two distinct ways, from 
the surface of liquids at all temperatures, and from all parts 
of liquids at certain fixed temperatures. The former is 
Evaporation, and the latter Ebullition, and each is gov- 
erned by fixed laws. 

535. Liquids are divided into two distinct classes; those 
which readily pass into vapor by the application of heat, 
such as ether, alcohol, and water; and those which decom- 
pose first, like the fats. Some solids, like camphor, pass 
into a vapor without becoming a liquid, and upon cooling 
again return to the solid state, a process called Sublima- 

536. Evaporation is the slow formation of vapor at the 
surface of liquids. It occurs at all temperatures, even 
below the freezing point of the liquid, but below a given 
temperature, its formation is extremely slow. The change 
goes on until the surrounding air is saturated with the 
vapor, or until all the liquid has disappeared. 

537. The rate of evaporation is increased by any me- 
chanical means which changes the surrounding air, for 
the vapor already formed is removed. Thus blowing 
across the surface of tea contained in a saucer removes the 
vapor and cools the tea. Some very volatile liquids, as 
bisulphide of carbon, or liquid carbonic anhydride,* evapo- 
rate with sufficient rapidity to cool the mass below freez- 
ing point, when the remaining liquid freezes from its own 

538. If a watch crystal containing ether be placed m 

*Often called carbonic acid. 



another containing a little water, and the ether be blown 
into with a glass tube, its evaporation so cools the water 
as to freeze the glasses together. 

539. So by blowing in a similar way, into a shallow 
vessel containing bisulphide of carbon, the bisulphide 
will freeze in the bottom of the vessel, from the reduction 
of temperature caused by its own evaporation. 

540. Vaporization in a Tacuum. To determine the laws 
which govern the formation of vapors in a vacuum, four 

barometer tubes are filled with 
mercury and inverted in a trough 
of the same, Fig. 174. One, A, 
serves as a barometer to measure 
the pressure of the air. A few 
drops of water are placed in B; 
of alcohol in D ; and of ether in 
E. The mercury instantly falls 
in the tubes, but different distan- 
ces, while the vapor of the sub- 
stance fills the place previously a 
vacuum. Hence the formation of 
vapors is governed by the follow- 
ing laws. 

I. — In a vacuum, volatile liquids 
instantly vaporize. 

Fig. 174. II. — At the same temperature 

and pressure, different vapors possess different elastic force. 

541. Ebullition. When the temperature of the liquid 
reaches a certain point, the formation of vapor is no longer 
confined to the surface, but takes place in all parts of the 
liquid. Bubbles of the vapor formed rise to the surface 
and escape into the air. This is Ebullition, or Boiling. 

542. Boiling Point. The pressure being 760 millimetres 



the boiling point of different liquids varies.* But when 
boiling commences, the temperature of the liquid remains 

543. Change of Boiling Point. Many causes influence 
the boiling point. Thus while pure water boils at 100° C, 
even minute quantities of salts in solution raise the boiling 
point. So also, the boiling point varies with the contain- 
ing vessel, differing in glass and copper. But the tempera- 
ture of the vapor formed is constant, since that depends 
upon the work to be done, or upon the weight of the col- 
umn of air to be raised. That is, the vaporization takes 
place against the pressure of the air upon the liquid. 

544. Laws. Boiling is governed by the following laws : 

I. — The toiling point varies as the pressure. 

II. — Whatever the intensity of the source of heat, the liq- 
uid remains of uniform temperature during boiling. 

545. Effect of Varying the 
Pressure. The effect of differ- 
ent pressure is well illustrated 
by a simple experiment with 
a glass flask, Fig. 175. Place a 
small amount of water in a large 
flask and heat it to boiling. 
Quickly cork the flask and re- 
move the source of heat. The 
increase of pressure at once 
stops the boiling. But invert 
the flask and pour a little cold 
water on the bottom, and the 
vapor condenses, relieving the 
IBBF pressure so that boiling begins 
Fig. its. again. 

*See Table VI. 




Will '"WW 


546. The Pulse Glass, Fig. 176, shows the low tempera- 
ture at which liquids boil when the 
pressure is removed. Two bulbs 
connected by a stem are partly filled 
with ether ; the air is removed by 
boiling the liquid, and the in stru- 
ng. 176. ment sealed by melting the glass. 
The condensation of the vapor leaves a vacuum, and the 
heat of the hand is sufficient to boil the enclosed liquid. 

547. The lowering of the boiling point by diminishing 
the pressure is well seen on the tops of high mountains. 
Thus upon Mont Blanc, the boiling point is so lowered that 
tea can not be made, nor eggs cooked by boiling in an 
open vessel. But both can be accomplished by using a 
vessel in which the steam can be confined, 
as in Marcet's Globe. So also, in many 
of the many common culinary operations, 
as in cooking doughnuts, a liquid is used 
whose boiling point is higher than that 
of water. 

548. Increased Pressure. Marcet's Globe, 
Fig. 177, shows the effect of increased press- 
ure in raising the boiling point. It consists 
of a copper globe with a manometer which 
dips into a little mercury placed in the 
bottom of the globe. Water is placed 
above the mercury, and a thermometer 
indicates the temperature, while a safety 
valve prevents all danger. When the 
globe is open to the air, the manometer 
indicates no pressure, and the thermome- 
ter stands at 100° C. When the globe is 
closed, the manometer rises, while the 
thermometer shows that the water is 
heated to a higher temperature. 


549. This principle is employed in Papin's Digester. 
This is simply a strong closed vessel in which water can 
be heated to a very high temperature. It is employed in 
extracting gelatine from bones and trimmings of hides; in 
preparing steam refined lard; and in similar processes re- 
quiring high temperature. 

550. Production of Cold. The expansion of a liquid to 
a vapor requires a large amount of heat. This becomes 
latent, that is, performs the work of moving the molecules 
further apart, and keeping them there. If the molecules 
are made to separate and the body expands without the 
application of heat, the temperature is lowered, and the 
vapor produced and the liquid from which it comes will 
take heat from surrounding objects. For this reason, a 
thermometer placed under the receiver of an air pump al- 
ways falls as the air is exhausted. 

551. Water Frozen by its own Evaporation. Leslie 
froze water by its own evaporation, using the apparatus of 

^^^. ^^ Fig. 178. A shallow glass vessel con- 
i «Hk Gaining sulphuric acid is placed upon the 

ijg^^plilllll plate of an air pump. A small brass or 
Fig. "ito" silver dish, carefully cleaned with alco- 

hol, and containing a little water, is suspended above it, 
and the whole is covered by a small receiver. Upon 
exhausting the air, a part of the water turns to vapor, 
which is absorbed by the sulphuric acid. The result is 
that the temperature of the water is lowered below freez- 
ing point. The rate at which any liquid turns to a gas is 
greatly increased by removing the pressure of the surround- 
ing air, while the boiling point is lowered. For this reason, 
in concentrating the syrup to make refined sugar, vacuum 
pans are employed, so that the air is exhausted and its 
pressure removed while the vapor is formed much more 
rapidly. The amount of pure white sugar produced is 
greatly increased by this means. 



552. The Cryophorus, Fig. 179, acts upon the same prin- 
ciple. This consists of two bulbs free from air, 
connected by a tube. The upper one is about 
half full of water, and the other is immersed in 
a freezing mixture. The water evaporates, and 
the vapor passes through the tube to the other 
bulb and is condensed. This takes place so rap- 
idly that the upper bulb is soon covered with 
frost, and the water in it frozen. 

553. Upon the same principle, porous vessels, 
called alcarrazas, are used in hot climates for 
cooling water. The outside is kept moist, and 
the evaporation cools the water. 

Fig. 179. 554. Ice Machines. These properties have 
been employed in the artificial production of ice. Two 
machines devised by Carre will show the general plan of all. 

555. One is simply a modification of Leslie's experiment. 
It consists of a cylinder made of an alloy of lead and an- 
timony, containing sulphuric acid, and connected with an 
air pump. The air is exhausted from a bottle about one- 
third full of water, and made to bubble through the acid 
on its way to the pump. After a short time, the water in 
the bottle freezes. 


The Ammonia Ice Machine, Fig. 180, consists of 
a boiler, Z, connected to a 
cooler, A, by a strong tube. 
The boiler contains common 
aqua ammonia. It is first 
placed upon a furnace and 
the cooler is placed in a tub 
of cold water, R. The heat 
liberates the gaseous ammo- 
Fig. 180. nia from the water, and it 



passes into the cooler, where it is liquified by its own pressure. 

557. When the liquif action is complete, the boiler is 
removed from the furnace and placed in cold water, the 
cooler is removed from the water and wrapped in dry flan- 
nel, and a cylinder containing water is placed in a hollow 
in the cooler. The water in the boiler quickly cools, and 
again absorbs the ammonia. This causes the liquid am- 
monia to turn again to a gas with great rapidity, so re- 
moving the heat from the water inside the cooler, which 
quickly freezes. 

558. Distillation. Since vapor from a solution consists 
of pure water, vaporization affords a ready method of re- 
moving impurities. The operation is called distillation. 

559. A Still, Fig. 181, consists of a large copper vessel, 
a, containing the liquid to be distilled. This is connected 
by a head and tube with a tube called a worm, coiled inside 

Fig. 181. 

a vessel of cold water. The liquid is vaporized in the 
boiler a and condenses in the worm. Since so much heat 
is rendered latent in forming a vapor, this must be given 
out in condensation: Hence to remove this heat, cold wa- 



ter must constantly run into the 
bottom of the vessel, while hot 
water escapes from the top. 

560. Liebig's Condenser, Fig. 
182, is used when only small 
quantities are to be distilled. It 
consists of a small flask, or re- 
tort, from which a tube passes 
downward through another tube, 
fitted with water-tight connec- 
tions. Water enters by a funnel, 
f , near the lower end, and escapes 
by an opening, g, in the upper 
part, while the condensed liquid 
falls out at the lower end. 

561. Fractional Distillation. 

Liquids of different boiling point 
mixed together, can be separated 
by distilling. That with the 
lowest boiling point is first re- 
moved, then the next, and so on. 
This process, called Fractional 
Distillation, is employed in re- 
fining petroleum to get naptha, kerosene, paraffine, etc. 

562. Moisture of the Air. Water constantly evaporates 
into the air. It follows that the air is never completely 
free from moisture. Nor is it often completely saturated, 
that is, so filled as to be incapable of dissolving more. The 
point of saturation, too, varies with the temperature, that 
is, with the elasticity. The amount of moisture which the 
air contains compared with the amount required to satu- 
rate it, is called the Hygrometric State. 

Pig. 182. 

563. Hygrometers are instruments for measuring the 



h} T grometric state of the air. They act either by cooling 
a body through evaporation, or by absorption. 

564. Daniell's Hygrometer, Fig. 183, consists of two 
glass bulbs connected by a glass 
tube bent twice at right angles. 
The larger bulb, A, is filled about 
two-thirds full of ether, and con- 
tains a delicate thermometer. 
The space above the ether con- 
tains only its vapor. The other 
bulb is covered with a piece of 
muslin. A thermometer on the 
stand gives the temperature of 
the surrounding air. 

Fi£. 183. 565. Ether is allowed to fall 

slowly upon the muslin, and by its evaporation, it cools 
the bulb. This condenses the vapor inside, and accelerates 
the evaporation in the other bulb, cooling it, until finally 
moisture begins to be deposited upon the bulb. The tem- 
perature at which this occurs is the dew point, and the 

elastic force of vapor at that tem- 
perature is the elastic force of 
the amount present in the atmos- 
phere. Dividing this by the elas- 
tic force of vapor at the tempera- 
ture of the atmosphere gives the 
hygrometric state. 

566. The Psychrometer, Fig. 
184, is used by the United States 
Signal Service to determine the 
hygrometric state. It consists of 
Fig. 184. two thermometers, the bulb of one 

covered with muslin, and kept moist by dipping in a vessel, 
of water. The difference of the two thermometers is taken 


and the percentage of moisture is then found in a table. 
In the one here shown, an index is added to show the rela- 
tive amount of moisture in the air. Such an instrument is 
commonly called the Hygrodeik. 

567. Hygrometers of Absorption are made of some sub- 
stance which absorbs moisture from the air. . Thus, if two 
figures are connected by a thread, the moisture of the air 
will twist the thread and force one of the figures forward. 
The little toy for determining the state of the weather 
often seen in shop windows is constructed in this way. A 
figure of a man and one of a woman are connected by a 
cord. In moist weather, the contraction of the cord draws 
the woman inside and forces the man out. In dry weather, 
the action is reversed. 

568. Clouds and Fog. When a warm current of air 
moving in one direction meets another current from a colder 
region, the warm current is chilled. This brings it nearer 
to the point of saturation. If it reach that point, the 
vapor becomes visible and forms a Cloud. A cloud resting 
upon the earth is called Fog. 

569. Rain, Snow and Hail. When a cloud has become 
sufficiently dense, the moisture begins to collect in minute 
drops which descend from gravity, increasing as they fall, 
until they reach the earth. This is Rain. 

570. If the cold current chills the warm sufficiently to 
cause the moisture to freeze as it condenses, it forms Snow. 
This usually occurs in the upper regions of the atmosphere. 

571. Sometimes drops freeze as they fall, often increas- 
ing after they have frozen. This is Hail. Regular hail 
stones are pear shaped, and are frozen in concentric layers. 
Irregular hail stones are formed by several hail stones 
freezing together, or by fracture. 

158 HEAT. 

572. Dew. The radiation* from the surface of the earth 
during the night cools the earth. When this reduces the 
temperature below the point of saturation of the atmos- 
phere, the moisture is deposited from the layers near the 
earth, and forms Dew. It is deposited most abundantly 
upon the blades of grass, and upon other pointed objects 
because they radiate heat most rapidly in proportion to 
to their mass, and so reach the lowest temperature. 

573. Frost. If the temperature descends below freezing 
point, the deposited dew solidifies and forms white or 
hoarfrost. The so called black frost is simply the freezing 
of the plants themselves without being covered by moist- 
ure, or with only a very thin layer. 

Section IV. — Spheroidal Co:nt>itio:n". 

574. If a drop of liquid is placed upon a highly heated 
metallic plate, it does not immediately boil, but rolls qui- 
etly around, and slowly evaporates. This is well illustrated 
by placing a drop of. water upon red hot iron, or a drop of 
ether upon heated silver or platinum. This is called Sphe- 
roidal Condition. 

igkm 575. If a drop of wa- 

ter be placed upon a 
heated plate, and a can- 
dle be placed beyond, 
Fig. 185, the light can 
be seen between the 
drop and the plate. 
Fi s- 185 - This shows that the 

liquid does not touch the plate, but rests upon a cushion of 
its own vapor. The non-conducting power of the vaporf 
prevents the liquid from reaching the boiling point. 

*See Sec. 539. 
tSee Section 583. 



576. But if the plate cools so 
that this cushion of vapor is no 
longer formed, the drop imme- 
diately evaporates with a slight 
explosion which scatters the drop 
in all directions, Fig. 186. 

577. Boiler Explosions. An 

experiment suggested by Dr. Tyn- 
Fig. 186. dall indicates that some explosions 

of steam boilers may be produced by the spheroidal condi- 
tion. A copper flask, Fig. 187, is fitted with a cork through 

which a small glass tube passes. 
The flask is first heated red hot. 
A small quantity of water is 
then poured in and it at once 
assumes the spheroidal condi- 
tion. The cork is then inserted, 
and all the steam formed escapes through the small tube. ■ 
But removing the flask from the source of heat, the 
water soon touches the flask, a large amount of steam is 
formed almost instantly so that the tube is no longer 
large enough to allow it to escape, and the cork is driven 
violently out. 

578. So, if from any cause, the walls and tubes of a 
steam boiler become so hot as to place the water in the 
spheroidal condition, when on cooling, the water once 
more touches the iron, sufficient steam would form to cause 
an explosion. 

Fig. 187. 





579. Heat travels in three ways. The heat from the 
source may be applied to one portion of the body to be 
heated, and the heat may then travel from molecule to mol- 
ecule, each molecule being heated : Conduction. Or, second, 
the molecules nearest the source of heat, may be heated, ex- 
pand, and then move to new positions, while others take their 
place: Convection. Or, third, the heat may pass from the 
source through the intervening space to some body to be 
heated, without heating the intervening medium : Radiation. 

Section I. — Conduction. 

580. Conduction is practically confined to solids, since 
the molecules of liquids and gases take new positions be- 
fore giving their heat to the contiguous molecules. Solids 
which thus transfer heat readily are Good Conductors : e. g. 
metals. Such solids are of nearly uniform temperature 
throughout their entire extent. Solids which do not trans- 
fer heat readily are Bad, or Non-Conductors: as glass and 
the resins. 

581. The Conductometer, Fig. 188, is used to show the 
difference in the conducting power 
of different solids. It consists of a 
brass box carrying a series of rods 
of different metals placed in the or- 
der of their conductivity. A small 
piece of wax is placed upon each, 
and the box is filled with hot water 
as the source of heat. The wax on 

the ends of the rods liquifies in the following order, Silver, 



Copper, Iron, Zinc, Tin, Lead, and lastly, Glass. This 
shows the order of the conductivity of these metals.* 

582. Homogeneous solids transmit heat with equal fa- 
cility in all directions. But if the molecules are arranged 
differently in different directions the rate varies. Thus a 
piece of wood conducts heat most readily in the direction 
of its fibers. So too, a crystal, the length of whose axes 
^^j^^ varies, conducts heat most rapidly in the direc- 
B^gl I tion of its longest axis. This is shown by cov- 
HL4 1 ering a section with wax, and heating its centre. 
^^^^^ Such a section made 

Fig. 189. perpendicul ar t o the 
longest axis shows a melting 
of the wax in the shape of a 
circle, Fig. 189: when the sec- 
tion is parallel to that axis, the figure formed by the melt- 
ing wax is in the shape of an ellipse, Fig. 190. 

583. Liquids and Oases conduct heat 
very slowly. This is readily shown by 
the apparatus of Fig. 191. A funnel 
shaped vessel has an air thermometer 
passing down through the neck and 
dipping in a vessel of liquid beneath. 
The funnel is then filled with water 
just over the bulb of the thermometer, 
and a layer of ether is poured upon the 
water and ignited. The heat is con- 
ducted through the water too slowly to 
affect the thermometer. 

584. In the same way, if a test tube 
containing a little water is placed in a 

W freezing mixture of ice and salt, the 
Fig. i9i. water freezes. Then the tube can be 

*For the conductivity of various solids, see Table "vTL 
N. P. ll. 

162 HEAT. 

nearly filled with water, and the water boiled in the upper 
part of the tube without melting the ice. So the tube 
contains at the same time, ice, cold water and boiling water. 

585. The non-conducting power of liquids prevents 
ponds and lakes from cooling to freezing point throughout 
their entire depth, in connection with the expansion of 
water below 4°C* The surface is cooled, but the mass 
beneath remains above freezing point. 

The non-conducting power of gases is applied in double 
walls and windows. The air between is confined, and re- 
tains the heat of the inner wall. 

So too, clothing is warm because of the air confined be- 
tween the layers. 

A similar application of the non-conducting power of 
porous solids which contain large masses of air is made in 
the Norwegian kitchen. The cooking is begun in a tin or 
copper vessel, which is then removed and placed in a box 
packed with felt. The non-conduction of the felt retains 
the heat for a long time. 

So also, a piece of ice is kept from melting by wrapping 
in flannel. 

Steam pipes are often packed in sawdust, plaster, or as- 
bestus for a similar reason. 

Section II. — Convection. 

586. Liquids and Oases are heated by Convection. ^-That 
is, the portion nearest to the source of heat becomes heated 
and expands, so diminishing its specific gravity. It then 
rises to the surface carrying the heat with it, while another 
colder portion takes its place. This is in turn heated and 
rises. Thus a series of currents is formed and continues 
as long as the heat is applied. 

* See Sections 527 and 528. 



587. The convection currents can be well shown by the 

apparatus of Fig. 192. A glass 
vessel is filled with water con- 
taining bran or flowers of sul- 
phur and heated. The motion 
of the bran then shows the 
heated current ascending in the 
middle, while the cold descend- 
ing currents appear near the 

588. Rooms are heated by 

convection of gases. The air 

near the stove is heated and 

Fig- 192. rises to the top of the room, 

while cold air takes its place. Thus a series of currents is 

set up, warming the room. 

The same principle is applied in hot air furnaces. The 
cold air is admitted to the furnace in the cellar from the 
external air. It is then heated, and rises through pipes to 
the rooms to be heated. So to accomplish this there must 
be some escape for the air already in the room, else the 
heated air cannot enter. 

Section III. — Radiation. 

589. Heat can also travel through an intervening me- 
dium to an object beyond, without raising the temperature 
of that medium. This is Radiation. Thus, a person stand- 
ing in front of a fire feels the heat of the fire. But if a 
screen be placed between him and the fire, he no longer 
feels it, because the screen intercepts the radiant heat. 

590. Ray. A ray of heat is the heat that passes along a 
straight line. 

A beam ox pencil is a collection pf rays, 




591. Luminous Heat is "heat from a source that also 
gives light, that is, has a temperature above the point of 
incandescence. Obscure, or dark heat is radiated from a 
source that is not luminous. 

Since Heat is one of the radiant forces, it follows the 
law of Inverse Squares.* 

592. Laws of Radiant Heat. Place a thermometer in 
different positions around a source of heat, hut at equal 
distances from the source ; it everywhere indicates the same 
temperature. Hence I. Heat is radiated in all directions 

593. If a screen be placed between the thermometer and 
the source of heat, the temperature no longer rises. Hence 
II. Heat is radiated in straight lines.f 

594. III. Laws of Intensity. The intensity of radiant 
heat is best measured by the Ther- 
mo-electric pile.J The instrument 
is arranged as in Fig. 193. A tin 
box with blackened sides, is placed 
in front of the open cone attached 
to the instrument, and water at 
10°, 20°, etc., is placed in the box. 
The deflection of the attached 
Galvanometer varies in the same 
proportion. Hence I. The inten- 
sity varies as the temperature of 
the source. 

Fig. 193. 595. Water is then placed in 

the box and kept of uniform temperature. The pile, with 

*See Sec. 80, page 22. 

tThis is confined to media of uniform density If the density varies, re- 
fraction takes place according to the laws developed under Light, Sec. 083. 
tFor its construction and use, see Electricity. 


the cone attached, is placed in front, and removed to dif- 
ferent distances. The deflection remains constant. But 
by producing the sides of the cone until the lines reach 
the box, it is seen that the area inclosed, that is, the sur- 
face which radiates to the pile, varies as the square of the 
distance. Hence Radiant Heat follows the law of inverse 
squares, or II. The intensity varies inversely as the square 
of the distance. 

596. If a screen containing an aperture be placed be- 
tween the box and the pile, the deflection of the galvan- 
ometer remains constant, at whatever angle to the pile 
the box be placed. But the area of the box opposite the 
opening increases as the angle increases. So then, the 
number of rays that can pass the aperture from a given 
surface must decrease as the angle varies from parallel 
with the screen. Hence III. The intensity varies with the 
obliquity of the rays. 

597. This last experiment explains the difference of heat 
on the earth's surface at different seasons of the year. For 
as the angle at which the rays of heat strike the earth's 
surface diminishes, the number of rays which meet any 
given area, diminishes. 

598. Theory of Exchanges. If a hot body be brought 
into a room, the temperature of all neighboring bodies is 
raised by radiation from the heated body. But if a cold 
body be similarly placed, the temperature of surrounding 
bodies is lowered. This process goes on until all bodies 
become of uniform temperature. Indeed, it does not stop 
then, but its effects are no longer apparent, since every 
body radiates the same amount of heat that it receives. 
This is called the theory of exchanges. 

A body is heated when it receives more heat than it 
radiates: cooled when it radiates more heat than it receives. 

166 HEAT. 

599. Causes which vary the Rate of Radiation. Heat 

is radiated only from the surface. Hence changes which 
vary the surface while the mass remains the same vary the 
rate of radiation. Thus, a polished hody will radiate less 
than a roughened surface, because the surface is really less. 

A stove is covered with graphite to increase the rate of 
radiation. It is polished for the sake of its appearance, 
though the polishing reduces the radiating power of the 

A dark body usually radiates better than a light one. 

600. Effect of Heat upon a Surface. When rays of ra- 
diant heat meet a surface, they may be Transmitted, Ab- 
sorbed, or Reflected. 

601. I. Transmission of Heat. Any body which will 
allow heat rays to pass is called a medium. No substance 
is known to allow all the heat to pass; nor indeed will any 
substance intercept all the rays. A body which will allow 
the greater part of the heat to pass through is called dia- 
thermanous ; one that intercepts nearly all is called ather- 
manous. Rock salt is the most diathermanous body known ; 
alum the most athermanous. 

602. A Burning Glass. Since heat is refracted the same 
as light, only when rays meet a surface at right angles, 
can they pass directly through. So a lens of glass, or of 
rock salt, will concentrate the heat rays, or bring them to 
a focus, the same as those of light.* Paper, or tinder? 
placed at the focus is inflamed. 

603. II. Absorption of Heat. Heat rays which meet 
the surface of a body, may enter that body, but fail to pass 
through. In this case, they expend their force in moving 
the molecules to a greater distance from each other, that 
is, in raising its temperature, and are said to be absorbed. 

♦See Light, Sees. 701 and 704. 



In general, bodies absorb heat readily that radiate it 
readily. Thus roughened and blackened surfaces absorb 
the most rapidly. 

60±. Franklin's Experiment. To test the influence of 
color upon the rate of absorption, Franklin placed pieces 
of cloth of different colors, upon the surface of clean snow, 
and allowed the sun's rays to fall directly upon them. 
Black absorbed the most, so that it quickly melted the 
snow and sank in the depression made. Other colors ab- 
sorbed less, until the white actually formed a protection 
to the snow, less melting under that than around it, so 
that in a short time, the cloth was elevated upon a heap of 

605. For the same reason, dark clothing absorbs more 
of the sun's direct heat than light, and is warmer. There- 
fore light clothing should be worn in summer, and dark 
in the winter. 

606. III. Reflection. The heat rays which meet a sur- 
face may be turned back from that surface. This is Reflec- 

607. Experimental Proof. The reflection of heat may 

Fig. 191 

♦For the laws of Keflection, see Section 382. 

168 - HEAT. 

be proved by using a concave reflector of polished silver or 
brass, Fig. 194. A tin cube with blackened side is placed 
before the reflector and filled with hot water as a source of 
heat, and a delicate thermometer is placed in the focus. 
The heat rays radiate from the cube to the reflector, and 
after reflection are brought to a focus upon the thermometer. 
The rays of heat can be traced in the same way as the 
sound waves in the Whispering Gallery.* 

608. Radiation and Reflection in a Yacuum. Heat is 

radiated and reflected readily in the vacuum produced by 
the air pump, for a current of electricity passed through a 
platinum wire which is placed in the focus of a concave re- 
flector under the receiver of an air pump, heats a thermom- 
eter at the focus of a second reflector. Probably, in a per- 
fect vacuum, heat would not pass. This has never been 
produced, and it seems likely is unattainable. 

609. Reflection of Cold. Since cold and heat are relative 
only, cold should appear to be reflected the same as heat. 
Thus, if a piece of ice be placed in one focus of a pair of 
reflectors, and a thermometer in the other, the thermome- 
ter falls. This result is explained upon the principle of 
exchanges. The thermometer simply radiates more heat 
than it receives, and so falls. 

Section IY. — Soukces of Heat. 

609. The sources of heat are of two classes: I, those in 
which the heat is produced by Chemical Action: II, those 
in which the heat results from Mechanical Action. 

610. I. Chemical Action. Nearly all chemical changes 
are accompanied by a change of temperature. When the 
chemical action is a union, the volume is usually diminished 
and heat is produced. When the volume increases, the 
temperature is usually reduced. 

*See Section 396. 



611. Combustion is the most familiar chemical change 
which produces heat. This is really a union of the oxygen 
of the air with the combustible. Flame is produced when 
the temperature is above the point of vaporization of the 
substance burning, when the gas produced burns. If the 
flame contains incandescent particles, it produces light. 

612. The Sun. The real source of tlte sun's heat is un- 
known, but many phenomena indicate that it is chemical 
action of some kind. It is certainly surrounded by enor- 
mous flames of incandescent gas, and these indicate chem- 
ical changes. Its present temperature is above the point 
of vaporization of iron, so that it is constantly radiating 
heat into space in all directions. The Stars are in a simi- 
lar condition. 

613. H. Mechanical Action. All mechanical action is 
accompanied by heat. This results either from friction, or 
from compression, which brings the molecules nearer each 

Fig. 195. 

614. The apparatus of Fig. 195 is used to prove the pro- 

170 HEAT. 

duction of heat by friction. A brass tube is screwed to a 
small pulley on the whirling table, and is made to revolve 
rapidly by means of a large wheel. It is then partly filled 
with water and corked. Friction is produced by the hard, 
wood clamp P, and this soons developes sufficient heat to 

boil the water. The steam generated then expels 

the cork. 


615. The Fire Syringe, Fig. 196, shows the 
production of heat by compression. It consists of 
a cylinder with a piston fitting nearly air tight. A 
little tinder is placed in a cavity in the end of the 
piston, and the piston suddenly driven down the 

Fig. 196. cylinder, and quickly removed. The compression 

of the air ignites the tinder. 

61 6. The relation of mechanical action to heat is shown 
by many familiar experiments. Thus, hammering a piece 
of iron heats it. Rubbing a nail or steel pen rapidly over 
a piece of wood develops heat. The Indians, and other 
savage tribes, kindle a fire by the friction of two pieces 
of wood. 

617. The relation of mechanical action and heat furn- 
ishes one of the best illustrations of Conservation of Energy: 
Heat, by means of the steam engine, is made to do mechan- 
ical work ; and in turn mechanical work produces heat. 
By no means at command, can the mechanical work of a 
steam engine be made to produce the original amount of 
heat, nor the theoretical heat power of the coal burned be 
equaled in the work of the engine, but sufficiently near 
approximations have been made to show that if all sources 
of loss could be removed, they would be equal. So all 
that man can do, is to cause energy to change its form at 
his will, and make it do his work. 




618. The amount of heat required to raise the tempera- 
ture of different bodies through a given number of degrees, 
varies. That is, the work required to move the molecules 
apart is not the same in all bodies. The amount required 
for any given body is termed its Specific Heat, and it is 
determined by comparison with some other body as a stan- 

619. Unit of Heat. The most convenient method of ex- 
pressing heat is by alteration of temperature. The stan- 
dard usually selected is water, both from its convenience 
and* because its specific heat is the highest of known sub- 
stances. Hence, the unit of heat is the heat required to raise 
one kilogramme of water through one degree centigrade. 

Section I. — Determination of Specific Heat. 

620. The Specific Heat of any body may be determined 
by either of two methods ; I. By Fusion of Ice; II. By 

621. I. Fusion of Ice. If a kilogramme of ice be placed 
in a kilogramme of water of the temperature of 79.25°, the 
ice melts and the water stands at the temperature of 0°. 
That is, 79.25 thermal units are required to change the 
condition of water. This heat is rendered latent, that is, 
is used in overcoming the inertia of the molecules. 

622. If a body be heated to any given temperature, on 


172 HEAT. 

cooling it again to zero, it gives out the same amount of 
heat as it received during the heat- 
ing. So Black took a block of ice 
about .3 of a cubic metre in size, 
bored a hole into it, and fitted a 
cover of ice, Fig. 197. He then 
heated the body whose specific heat 
was required, using by preference a 
small sphere, to a certain tempera- 
Fif? - 197 - ture, and dropped it into the hole 

and put on the cover. After the ball was cooled to zero, 
the ball was removed, the water carefully wiped out by a 
piece of sponge previously weighed, and the sponge again 
weighed. This gave the weight of the water. Now since 
one kilogramme of ice in melting uses 80 units of heat, P 
kilogrammes would use 80P units of heat ; that is, the 
body gave out 80P units of heat. Its specific heat would 
be 80P divided by the product of its mass and temperature. 
Let m be the mass, t the temperature, and S the specific 

heat. S=*5 

623. II. By Mixtures. The body is first heated to a 
given temperature, and then plunged into cold water whose 
mass and temperature are known. The body is cooled, 
while the water is heated. After they arrive at the same 
temperature, the specific heat is calculated as before. 

624. The high specific heat of water is of great benefit 
in moderating climate. Since so much heat is required to 
warm the water, the temperature is more equable in the 
vicinity of large bodies of water, as the ocean, lakes and 
ponds. Forjhe same reason, the freezing of ponds and 
lakes during extreme cold weather much shortens its du- 
ration. But when the ice again melts, the process is re- 
versed, an equal amount of heat is rendered latent, and 
the change from cold weather to warm is rendered more 


Section IT. — The Steam Engine. 

625. The Steam Engine is a machine for converting the 
elastic force of steam generated in a confined space, and so 
compelled to absorb a large amount of heat, into mechani- 
cal motion. Water is used preferably to other liquids 
because of its high specific heat. In one form of compound 
engines, bisulphide of carbon is used, the liquid being heated 
by the steam exhausted from the first engine. The steam 
engine depends upon the mechanical equivalent of heat for 
its action. 

626. Determination of the Mechanical Equivalent of 
Heat. Several experimental physicists have determined the 
mechanical equivalent of heat. The experiments of Messrs. 
Mayer and Joule have proved the most important. 

627. The conversion of heat into mechanical motion, 
and the converse, had long been noticed. Their intimate 
relation had been shown by a variety of experiments like 
the fire syringe, and boiling water by friction.* But such 
simple experiments, while demonstrating the principle, 
gave no quantitative results. 

628. Thus air compressed into a receiving chamber is 
sensibly heated. If it is allowed to escape into the air 
after cooling to the temperature of surrounding objects, it 
is sensibly cooled by its expansion. Blowing upon the 
face of a thermo-electric pile by a pair of bellows raises the 
temperature, because the mechanical motion of the bellows, 
arising from the force applied to the handles, is directly 
employed to bring the molecules of air nearer together. 

629. Two of the most interesting experiments were made 
by Sir Humphrey Davy. His attention was called to the 
heated condition of the turnings produced in boring can- 

*See sections 613 and 615. 



non, and to test the source of heat, he caused a piece of 
metal to be turned inside of a large gun, while a quantity 
of cold water was placed outside. In a few hours, the wa- 
ter boiled from the heat developed by the friction of the 
two pieces of metal. For a second experiment, he fixed a 
cylinder of ice so that it could be turned in a block of ice, 
while the temperature of the surrounding air was zero. In 
a short time, the ice melted. 

630. All these experiments, while showing the principle 

clearly, fell short of nu- 
merical determination. 
Joule accomplished this 
by using the apparatus of 
Fig. 198. 

A roller C is made to 
revolve by the descent of 
the weight G, and in its 
turn it causes A to revolve 
by a cord. The distance 
of the descent is meas- 
Fig. 198. ured by a scale at G. The 

cylinder A turns a stirrer consisting of paddles P, (shown 
in section at V) placed in a copper vessel, filled with 
water. The increase of temperature measures the amount 
of heat generated. By a series of experiments with this 
apparatus, Joule determined the value of the thermal unit 
on the Centigrade scale as 1.395 foot-pounds: on the Fahr- 
enheit scale as 772 foot-pounds. 

631. The Steam Engine consists essentially of a boiler 
and a cylinder. The steam after doing its work, may escape 
directly into the air, which makes the engine High Press- 
ure, or it may escape into a condenser, when the engine is 
Low Pressure. The former is used when the space is con- 
fined, or the fuel cheap: the latter, when saving fuel is 



632. The Boiler consists of a strong rolled iron cylinder 

in which the water is 
placed. Flues or tubes 
pass through the wa- 
ter, one end opening 
in the fire box, and the 
other into the chimney, 
to increase the radi- 
ating surface. A tubu- 
lar boiler is shown in 
section in Fig. 199. 

**• 199 - The fire is placed at 

A, and the gases reach the chimney at B, through the tubes. 
A safety valve is placed upon the top of the boiler to allow 
the steam to escape before the pressure exceeds the point 
of safety. 

The steam is taken from a dome E placed upon the top, 
and carried by a pipe to the cylinder. The dome prevents 
the steam from carrying water forward with itself, and 
makes the steam dry. 

633. The Cylinder. Fig. 200, is a section of the cylinder. 
C is the cylinder, in which a piston P 
now descending, moves steam tight. The 
steam is supplied by the pipe S, and passes 
in above the piston around the rod of the 
valve moved by the rod m, while the steam 
below the piston escapes through the pipe, 
valve and escape pipe 0. When the piston 
reaches the bottom of the cylinder, the 
valve is moved upward, closing the entrace 

Fig. 200. pip e aim opening the discharge pipe to 

the top of the cylinder, and opening the entrance pipe to 
the bottom. 

634. The Eccentric moves the valve. This is simply a 
circle placed upon the shaft which the piston moves, whose 



centre does not coincide with the centre of the shaft. This 
gives a back and forward motion to the valve rod, as the 
shaft revolves. 

Fig. 201. 

635. Fig. 201 gives the details of the low pressure en- 
gine: c is the steam pipe; P is the«piston, which connects 
with the crank K, and balance wheel V, by the walking- 
beam L. The steam escapes into the condenser 0. An air 
pump M, exhausts the air and hot water from this receiver. 
Cold water continually pours into the condenser through 
a pipe, driven in by the pressure of the external atmos- 
phere upon the surface of the surrounding cistern. It is 
fed to the cistern by a forcing pump. Q is a forcing pump 
used to supply the boiler. The governor consists of two 


heavy iron balls joined to a shaft, which move apart as 
they revolve and control the amount of steam supplied, by 
closing a valve in the supply pipe as they move apart. The 
pumps are all worked by the walking beam. The value is 
moved by the eccentric attached to the shaft of the bal- 
ance wheel. 
The high pressure engine omits the condenser and pumps. 


1. Section 503. When the Centigrade thermometer 
indicates 30°, what temperature is indicated by the Fahr- 
enheit scale? 

2. When the C. scale indicates - — 20°, what is the reading 
of the other scales ? 

3. When the F. scale reads — 40°, what is the reading 
of the Centigrade? 

4. When Reaumur's scale reads — 25.6°, what is the 
reading of the other scales ? 

5. Section" 495. If the coefficient of linear expansion of 
iron is .0000122, what must be the length of a rod to ex- 
pand 1 millimetre for each degree of increase of tempera- 

6. An iron suspension bridge is to be erected 81,967 feet 
long. What amount must be allowed for expansion at 
each end of the bridge, considering the extreme limit of 
the change of temperature to be 30°? 

7. Sections 217 and 497. The specific gravity of mer- 
cury is 13.6. Required the volume of 60 kilogrammes. 

8. The coefficient of cubic expansion of mercury is 5-5V o". 
Required the volume of 50 kilogrammes at 70°. 

n. p. 12. 

178 HEAT. 

9. Sections 217 and 528. The s. g. of ice being .92, what 
will be the volume of water at 4° made by melting 100 

litres of ice ? 

10. A recent patent for making ice in blocks from the 
freezing of water in the external air in cold weather 
requires the opening of the shell of ice formed outside by 
the first water frozen, and the removal of some water from 
the inside. How much must be removed from a block 2 ft. 
long, 1 ft. high and 1 ft. wide ? 

11. Required the weight in grammes of the water re- 
moved in problem 10. 

12. Section" 594. A thermometer placed in front of a 
stove rises 25° ; another at the same distance from a lamp 
rises 5°. What is the ratio of the temperature of the two 
sources of heat ? 

13. Section 595. The face of a thermo-electric pile is 
exposed to the heat radiated from a distant fire, and the 
open cone is removed ; the attached galvanometer is de- 
flected 20°. The pile is then removed 100 metres and 
exposed a second time ; the deflection is now 10°. Con- 
sidering the deflection to vary as the intensity of the heat 
received, determine the distance of the fire. 

OPTICS. 179 

Part III. — Optics. 

636. Introduction. When transverse vibrations of cer- 
tain definite lengths reach the retina of the eye, they give 
rise to the sensation of sight. The science of Optics treats 
of the phenomena pertaining to these vibrations, and the 
laws which govern them. 

637. Ether. All space is believed to be filled with a 
peculiar kind of matter of extraordinary elasticity, called 
ether. Undulations in this ether transmit light from its 
source to the object which is illuminated. 

638. Luminous Bodies give light of themselves, that is 
produce the luminous undulations. Those which do not 
are called Non-Luminous. 

Ray. A ray of light means the undulations which move 
along a straight line. 

A Beam or Pencil is a collection of rays. Rays which 
separate are called Divergent; those which approach each 
other are Convergent. 


Section I. — Sources of Light. 

639. The principal sources of light are the Sun and 
Stars, and chemical action upon the earth. Recent investi- 
gations indicate that the incandescent state of the heavenly 

180 OPTICS. 

bodies which makes them sources of light is associated 
with, and perhaps results from chemical action. 

640. The Sun is the great source of light for the solar 
system. Its intensity surpasses that of all artificial lights, 
so that they appear dark spots when placed between the 
eye and the Sun. 

641. The Fixed Stars are similar in many respects to 
the Sun. During the day, their light is obscured by the 
more intense light of the Sun. It is not however absent, 
as can be seen by looking at the sky from a deep well, 
when the stars become visible, because reflected light is 
cut off. Besides, it is not nearly as dark on a clear night 
as when the light of the stars is obstructed by clouds. 

642. Chemical Action. Intense chemical action devel- 
opes light, and most such cases are accompanied by com- 
bustion. But the light is produced by particles not actu- 
ally consumed, though rendered incandescent. 

643. The condition of a luminous flame is well shown 
by pressing a piece of stiff paper, or better of wire gauze, 

^^-^ down upon the flame of a candle, Fig. 

WL"~''43l~^£\ ^^' Such an experiment shows that 

jpFT-V j a the cen tre is dark, while a ring of fire 

III encloses it. The reason is that some of 

Fig. 202. the substances, those which contain 

large amounts of hydrogen, are burned first, in the central 

part of the flame. This heats the carbon to the point of 

incandescence, while the carbon itself burns outside of the 

point of light. The carbon deposited upon any cold body 

placed in a flame shows that it is not itself consumed. 

The gas formed by the heat forms an interior cone, 
which does not burn. Outside of that is a pari where 
hydrogen burns, containing heated particles of carbon. 
Around that, is the section of burning carbon. 


644. A flame which does not contain heated but uncon- 
sumed particles is not luminous. Thus the flame of a com- 
mon spirit lamp gives very little light. It may, however, 
be rendered luminous by dropping into it some iron filings. 
So too the solid flame of the oxyhydrogen burner can be 
scarcely seen. But by placing a piece of lime in it, the 
lime is heated to incandescence, and the Drummond or 
Calcium Light is produced. 

645. Phosphorescence. A peculiar property shown by 
phosphorus and some similar substances is called phos- 
phorescence. The term is used for two series of phenome- 
na due to different causes. 

A number of bodies, after being exposed to a bright 
light, shine for some time afterwards. The sulphur com- 
pounds of calcium, strontium and bariuui, and certain 
minerals, notably the diamond and fluor spar, possess this 
property. It results from absorption of light by the body, 
which is given out again after the source of light is 

646. In a similar way, a piece of phosphorus, which is 
very slightly exposed to the action of oxygen, emits a 
faint light in a dark room. This is well shown by the 
so called " harmless fire. 1 ' A few small pieces of phosphor- 
us are placed in a bottle of sulphuric ether and allowed 
to dissolve. If then the ether be rubbed upon the hands 
or the face, the part seems on fire, though the effect is cool- 
ing, rather than heating. 

On the same principle, the light used in powder mills 
consists of a bottle of olive oil in which a piece of phos- 
phorus is placed. The oil dissolves a little of the phos- 
phorus. Upon removing the cork and allowing a little 
air to enter, and then shaking the bottle, the dissolved 
phosphorus emits a faint light. 

647. In like manner, some kinds of decaying wood, fish- 

182 OPTICS. 

bones, or certain gelatinous organisms shine as they undergo 
decomposition. For this cause, the surface of the ocean 
sometimes seems as though on fire. 

These latter phenomena are produced by the chemical 
changes going on in the body. The light emitted by the 
glow-worm and the lightning bug is probably caused by 
the chemical changes in a secretion called noctilucene. 
But they occur at so low a temperature that they seem 
allied to true phosphorescence. 

Section II. — Movement of Light. 

64:8. Light moves so rapidly that its passage between 
two points upon the surface of the earth appears to be in- 
stantaneous. Observations upon Jupiter's satellites made 
by Roemer in 1675 demonstrated that it does not. 

Roemer discovered that the calculated time for the 
eclipse of Jupiter's satellites varied from the observed to 
the extent of 16 minutes and 26.6 seconds. He found the 
cause of this in the different positions of the earth in its 

Fig. 203 shows the reason for this. J is the planet, and E its 
satellite approaching the shadow of the planet. When the earth 
is at T on the side of its orbit nearest Jupiter, the length of the 
ray which reaches it from the satellite is ET. But if the earth be 

Fisr. 203. 

at R on the opposite side of its orbit, the ray is ER. This is 
longer than ET by the distance bT, the diameter of the earth's 
orbit. If now the time of the eclipse was calculated for the point 
T, when the earth is at R, the eclipse occurs 16 minutes, 26.6 sec- 


onds after the calculated time: but if the time is calculated for K, 
it occurs 16 minutes 26.6 seconds before the calculated time, pro- 
vided the earth be at T. That is, light occupies 16 minutes 26.6 
seconds in crossing the earth's orbit, or 8 minutes 13 seconds in 
coming to the earth from the sun. 

649. The above observation gives light a velocity of 
about 190,000 miles per second. Since that time, the ve- 
locity of light in air has been determined by direct experi- 
ment, and has been proved to be slightly less than the 
above rate. Its velocity has also been determined for other 
gases, for liquids and for solids, and has been found to di- 
minish with the density of the body. 

650. Intensity of Light. This involves two questions ; 
the intensity of the light which falls upon an intercepting 
surface; and the intensity of the source of light. 

651. Light Propagated in Straight Lines. If a lamp 
surrounded by a sheet iron chimney be placed in front of 
the eye, a single spot of light is visible. If several cards 
containing small holes be placed between the eye and the 
hole in the chimney, the light is visible when the holes 
make a straight line. But if the hole in one card be out 
of the straight line, the light becomes invisible. This 
proves that light moves in straight lines, provided the me- 
dium is homogeneous. 


652. A luminous body is seen in all directions. Hence 
the light given off by a luminous body consists of diver- 
gent rays. This holds true of bodies of all dimensions. 
Hence a luminous surface may be considered as made up 
of a series of luminous points, each of which gives off 
divergent rays. 

653. Shadows result from the interception of these 
divergent rays. If rays of light are intercepted by an 
opaque bodj^, darkness exists beyond that body. This space 
where light is wanting is called the Umbra, or complete 



shadow. Around this, is a space where the light is only 
partly intercepted, where a part of the luminous body can 
be seen. This is the Penumbra. 
Shadows present the following cases. 

654. I. A Luminous Point, 

Fig. 204. 

whose light is intercepted 
by an opaque body, as 
a sphere. Here the 
shadow, or Umbra, is 
determined by lines 
drawn from the point 
tangent to the sphere, 
Lac and Lbd, Fig. 204.* 

That is, the Umbra 
is the frustum of a cone 
whose apex is at the luminous point. A section of the 
shadow made by a screen perpendicular to the axis of the 
cone, as S, is a circle. There is no Penumbra. 

655. II. A Luminous Body Smaller than the Opaque. 

In this case, the Umbra is determined by drawing lines 

tangent to both 
bodies. It is the 
frustum of a cone 
whose apex is at the 
point P, Fig. 205, 
where the tangents 
Fig. 205. meet, beyond the 

luminous body. A section made as in case I, is a circle. 
Tangents can also be drawn which cross between the bod- 
ies. These tangents determine the Penumbra, which sur- 
rounds the Umbra, ace, and bdf of the figure, and its 
section is a ring surrounding the Umbra. 

656. III. Luminous and Opaque Bodies of the same 

*This and all the views of shadows are shown in plane section. 



Diameter. This is a purely hypothetical case, and is deter- 
mined like case second. The Umbra is a cylinder. 

657. IT. The Luminous Body Larger than the Opaque. 

The Umbra and Penumbra are determined as before. But 

now the apex of the cone is 
beyond the opaque body, at 
P, Fig. 206, and the Umbra 
constantly diminishes in di- 
ameter until it reaches the 
apex. The Penumbra in- 
Fig. 206. creases and extends to an 

infinite distance. This is the most important case, as the 

shadows of the planets are determined by it, and eclipses 

require its application. 

658. Images by Small Apertures. Since every point of 
a body which acts as a source of light gives off divergent 
rays, a certain number of rays must reach an aperture. It 
follows that if the aperture be small, the rays will cross in 
the aperture and form an inverted image beyond. 

Fig. 207 shows this. A di- 
vergent pencil of rays starts 
from the point A and passes 
the aperture of the box O. 
They then continue in the 
same line, and reach a, where 
they form an image of that 
Fig. 207. point. In the same way, 

rays start from B, pass the aperture and form the point at b. Sim- 
ilarly, rays start from all the intermediate points and form the 
image of the entire object in an inverted position 

659. Laws of Intensity. Since light is a radiant force, 
it conforms to the general laws of radiant forces. That is 
I. The intensity of light varies inversely as the square of 
the distance from the source. II. The .intensity of light va- 
ries with the obliquity of the intercepting surface. 



660. Light furnishes the best means of proving the law 
of inverse squares. 

For if a piece of paper or board 
whose side is unity, Fig. 208, be placed 
at a distance of unity from the source 
of light, its shadow will just cover an- 
other whose side is two, placed at twice 
the distance: or whose side is three at 
three times the distance. That is, the 
light, which falls upon the larger ob- 
ject is all intercepted by one whose 
Fg. 208. area is one-fourth or one-ninth itself. 

Or, the light which reaches any given area at the distance of unity 
is four times that which the same area receives at twice that dis- 

The second law is proved by allowing a beam of light 
to pass through a small aperture and fall perpendicularly 
upon a surface beyond. If the surface be inclined, a larger 
area is illuminated. But no more rays can pass through 
the aperture, so that the intensity is diminished. 

661. Photometry, The art of measuring the compara- 
tive intensity of different lights is called Photometry, and 
the instruments for measuring, Photometers. 

Unit of Light. Lights are measured by comparing their 
intensity with the light given by a sperm candle burning 
at the rate of two grains per minute. This unit is called 
a Candle Power. 



Fig. 209. 
662. Rumford's Photometer, Fig. 209, consists of a screen A, in 


front of which is placed a black rod B. A candle burning at the 
rate mentioned above is then placed in front of the rod, a little to 
one side, and the light whose intensity is to determined is placed 
a little to the other side. This last light is then moved until the 
two shadows cast by B are equally dark. The distance of each 
light is then measured, and th'jir comparative intensity is inversely 
as the square of the distance. 

663. Bunsen's Photometer is an improvement upon 
Rumford's. To determine exactly the point where both 
shadows are equal requires great skill. Bunsen removed 
this difficulty by placing the lights at opposite ends of a 
graduated scale, and placing between them a disc coated 
with wax, except a small >spot in the centre. The wax al- 
lows the transmission of light, so that the centre appears 
light on a dark background if the stronger light is in 
front of it, and dark on a light background if the more 
intense light is beyond. It is then moved until the spot 
disappears, when both sides are equally illuminated. The 
comparative distance of the two lights determines the in- 
tensity, as before. 

664. Wheatstone's Photometer, Fig, 210, consists of a revolving 
brass bead. The light reflected from it produces a curve, and 
this remains visible for a short time. With two lights of different 

Fig. 21G. 

intensity, two curves of different brightness are produced. The 
lights are then moved until they are uniform and the distance of 
the lights measured. Their intensity is then determined by Jhe 
law of inverse squares. The curves are shown at the right. 


188 OPTICS. 



665. When luminous vibrations reach the surface of a 
body, either of three things may occur. I. The light may 
be Absorbed, that is changed into some other form of mo- 
lecular motion. II. The light may be Reflected, that is 
turned away by the surface of the body. III. The light 
may be Transmitted, or pass directly through. The first 
needs no discussion. 

Section I. — Reflection of Light. 

666. Irregular Reflection. The surface which reflects 
light may be so rough as to send the light in all directions. 
So wherever the observer be placed, some light reflected 
from the object will reach his eye and enable him to see it. 
This is Irregular Reflection, and without it bodies would 
be invisible. The ordinary diffused day light results from 
this reflection from the particles of air and from the sur- 
face of bodies. 

r 667. Regular Reflection. The reflecting surface may be 
nearly regular, that is a portion of a plane, or some other 
regular figure. In this case, the light will be reflected to 
some definite position. This is Regular Reflection. 

668. General Laws of Reflection. If a mirror be placed' 
horizontally so that a beam of light entering a small 
aperture can reach it, the light is reflected to the opposite 
wall. Hence I. The Incident and Reflecting mys are in a 
plar^e perpendicular tq the reflecting surface. 


669. If now a small mirror, Fig. 211, be placed at the centre of 

a graduated circle, and a line be 
drawn perpendicular to the mirror, 
when a beam of light reaches the 
mirror, the angles upon both sides 

Fi£. 2ii. oi the perpendicular are seen to be 

equal. This is true at whatever angle the incident beam reaches 
the mirror. 

Hence, II. The angles of Incidence and Reflection are equal. 

670. Mirrors. Metals with a polished surface reflect light 
regularly, and form images of objects placed before them. 
A reflector of this kind is called a metallic mirror or speculum. 

Common mirrors consist of glass coated on the back 
with a metallic amalgam. The principal reflection is from 
the metallic surface, but the surface of the glass towards 
the object also reflects some light, so forming a second 
faint image, and obscuring the effect. 

Mirrors are of various shapes, as plane, cylindrical, con- 
cave or convex. 

671. Axes. Lines drawn perpendicular to mirrors are 
called axes. If a mirror have a focus, that is a point to 
which all the rays of light converge, the mirror is regular, 
In spherical mirrors, the axes pass through the centre, and 
the axis which passes through the principal focus is called 
the principal axis. All others are secondary axes. 

672. Images formed by Plane Mirrors. I. A Luminous Point. Let 

a luminous point A, Fig. 212, be placed in front of a plane mirror, 
M N. A pencil of divergent rays passes 
from the point to the mirror. These rays 
strike the mirror at all points, but any 
two, as those which enter the eye, will 
show the conditions of all. The ray AB 
strikes the mirror sit B, making the angle 
of incidence ABD, and is reflected mak- 
ing the angle of reflection DBO equal to 
it. It then reaches the eye and appears 
to come from the point a behind the mir- 
Fig. 212. ror, where the ray meets the axis passing 

190 OPTICS. 

through A. Similarly, the ray AC, by reflection, reaches the eye, 
and appears to come from a, for the eye sees every ray in the di- 
rection in which it enters it. So the light appears to be as far 
behind the mirror as it really is in front. 

673. II. An Object. Let an object AB be placed in front of a 
plane mirror MN, Fig. 213. Each point then becomes a source of 

light, and may be traced as in 
Case I. By drawing secon- 
dary axes from the ends, and 
tracing the rays which enter 
the eye, the position of the 
image is found. The ray AG 
meets the mirror at G, making 
the angle of incidence AGE, 
and is reflected at an equal 
angle to the eye. Tracing the 
Fig. 213. ra y back of the mirror until 

it meets the axis, the point A is found at a. So the ray reflected 
from H meets the axis BC at b, where the point B is found. 

The image is then as far behind the mirror as the object 
is in front of it. It is a virtual image, because a screen 
placed where the image is would receive no light. When 
an image would be formed on a screen, it is real. 

674. On this principle, a person standing beside a pond 
sees the objects upon the bank reflected from the water in 
an inverted position. The points nearest the water seem 
nearest after reflection, so that trees and other objects have 
their tops turned downward. 

A person standing in front of an upright plane mirror 
can see his whole body if the mirror is one-half the length 
of his body. The reason is that the rays of light from his 
feet which are reflected to his eye meet the mirror at a 
point half way between his eye and feet. For this reason, 
the lower half of mirrors reaching to the floor is valueless, 
except for ornament. 

675. The Kaleidoscope. If two mirrors be placed at a 
right angle to each other, a luminous body placed between 



them is repeated by reflection three 

Let O, Fig. 214, be a source of light. 
The ray OC reaches the eye at E, 
placing the image at 0'. So the ray 
OA is reflected from A to B, and from 
B to the eye, so giving the image O". 
The ray OD is also reflected to the eye 
producing an image at O"', so that 
the eye sees the original source of light 
Fig. 214. and three reflected images. 

The Kaleidoscope applies the principle of multiplied im- 
ages. It consists of three plane mirrors placed at angles 
of 60° with each other. A few pieces of variously colored 
glass are placed between, and light admitted through the 
end opposite the eye. The light from the pieces of glass 
and the various reflections then combine to produce regu- 
lar figures. The number made is very great, and some of 
them are wonderfully beautiful. 

676. Concave Mirrors are usually either sections of a 
hollow sphere or of a paraboloid. The former will show 
the principle of all. 

677. Focus. Rays of light reflected from concave mir- 
rors meet at some point called a Focus. 

Principal Focus. Rays of light from a body at an infi- 
nite distance from the mirror, as the Sun and Stars, are 
parallel. The point where such rays meet when parallel to 
the axis is called the Principal Focus. 

Fig. 215 
Fig. 215 shows how the principal focus is determined, The par 
allel rays meet the mirror M' at the points a, b, c, d, etc. Eadii 

192 OPTICS. 

drawn to these points give the angles of incidence, and the rays 
are then reflected, making the angles of reflection equal to the 
angles of incidence. They then meet at F the principal focus. This 
is half way between C and E. 

This discwssion shows that the principal focus is upon 
the principal axis, midway between the centre of curvature 
and the mirror. 

678. Secondary Foci. If the light be brought nearer the mirror 

the rays diverge, as 
LK, LI, etc., Fig. 
216. The focus is 
found as before, by 
drawing the radii C 
K, etc. , and making 
the angles equal. 
Fig. 216. It is at 1, further 

from the mirror than the principal focus F. 

The reasoning demonstrates that bringing the light 
nearer the mirror removes the focus to a greater distance 

If the light be brought to the centre C, all the rays are 
perpendicular to the mirror. They are then reflected di- 
rectly back to the source of light. 

When the light is placed nearer the mirror than the 
centre, as at 1, the focus is removed beyond the centre to 
L. These two points Land 1 are called Conjugate Focii, 
because rays from a source of light placed at one meet at 
the other. 

So again if the light be placed at the principal focus F, 
the reflected rays are parallel. 

079. Formation of Images. The image of an object 
placed in front of a concave mirror can be found by con- 
sidering each point of the object as a source of light, and 
tracing the point of meeting of the rays. 

Let AB, Fig. 217, be an object placed before the concave mirror 
MN. Draw secondary axes from the points to be found, as the 



extremities A and 
B. For if these be 
determined, all in- 
termediate points 
will be on the line 
joining them. The 
secondary axes are 
Fig. 217. AFandBG. Then 

draw rays from the points A and B to the mirror, as Ar and Bs. The 
radii to the points of meeting, Cr and Cs, give the angles of inci- 
dence, and the angles of reflection are eqnal. The reflected ray 
traced from r until it meets the secondary axis AF fixes the point 
A at A' . Bis similarly found at B' . 

So when the object is beyond the centre, the image is be- 
tween the centre and the principal focus, is real, inverted, and 

680. All images are found in a similar way. If the 
object be placed at the centre, there is no image: if be- 
tween the centre and the principal focus, it is magnified: if 
between the principal focus and the mirror, it is a virtual 

681. Convex Mirrors. A convex mirror is a section of 
a sphere which reflects from its exterior surface. The foci 
of such mirrors are found in the same way as with concave 


Fig. 218 shows the 
focus F of parallel 
rays. The perpen- 
diculars Ca,Cb, etc. 
are drawn through 
the mirror. 

Fig. 218. The ray Ar is 

reflected in the direction rH, and traced back meets the 
principal axis at F, half way between the centre and the 
mirror. But a screen placed at F would receive no light. 
The focus is then virtual, and behind the mirror. 

N. P. 13. 

194 OPTICS. 

682. Images by Convex Mirrors. These are found as in concave 

mirrors by tracing rays 
of light, Fig. 219. To find 
the position of the point 
A, draw the secondary 
axis AC. The ray AD is 
reflected making the an- 
gle of reflection equal to 

Fig. 219. the angle of incidence, 

and traced behind the mirror, meets the secondary axis, at a. In 
the same way, B is found at b. 

The image made by such a mirror is then smaller than 
the object, is direct and virtual. 

Section II. — Refraction. 

683. Definition. Light which passes obliquely from one 
medium to another of different density is bent at the sur- 
face where the two media come in contact. When pass- 
ing to a medium of greater density, the waves move slower, 
and the light is bent towards a perpendicular to the sur- 
face. When the light passes to a medium of less density, 
the rays are bent from the perpendicular. This change of 
direction is called Refraction. 

684. Refaction Shown. A glass vessel placed in the 
path of a beam of light allowed to enter a dark room by 
a small opening, clearly shows refraction. The path of 
the light before reaching the water can be seen by irregular 
reflection from the dust diffused in the room. Reflection 
from the molecules of the water shows the path of the 
light in the water. The change of direction takes place 
at the surface of the water. 

685. Laws of Refraction. Refraction agrees with reflec- 
tion in its First Laic: The angles of incidence and refrac- 
tion are in a plane perpendicular to the surface. 

To determine the Second Law, some instrument for com- 


paring angles is required. A simple 
apparatus is a square glass vessel 
used as shown by Fig. 220, for exam- 
ple, a square bottle, covered with stiff 
paper, with a circle cut out on one 
side. Two diameters, AB and DE, 
one horizontal and the other perpen- 
dicular, are then drawn, and water 
poured in until it just reaches the 
horizontal diameter. A beam of 
light is next admitted, preferably by 
a horizontal slit, and the apparatus 
placed so that it reaches the surface of the water at the 
centre of the circle G. The path of the rays can be clearly 

Now measure the perpendicular from the point where 
the beam of light crosses the circle H, to the perpendicu- 
lar diameter, that is HI, the sine of the angle of incidence, 
and FGr, the sine of the angle of refraction. Divide one 
by the other. Now by any means, as a mirror, change the 
angle of incidence, and measure as before, and find the 
ratio; it is the same as at first. Hence the Second Law: 
The ratio of the sines of the angles of incidence and refrac- 
tion is constant for any given media. 

686. Index of Refraction. The ratio of the sines be- 
tween any two media is called the Index of Refraction. It 
must be determined for every substance experimentally, and 
it differs very much in different substances. The diamond 
has the highest index of refraction; and bisulphide of car- 
bon stands very near to the diamond. 

687. Effects of Refraction. Some familiar phenomena 
result from refraction. Thus a stick placed partly in the 
water appears broken at the surface, and the part below is 




So a coin, Fig. 221, 
just hidden from the 
eye at E by the side 
of a basin is brought 
into view by filling 
the basin with water. 
The ray which starts 
in the direction ml is 
refracted downward 
at I so that it reaches 
Fig. 221. the eye at E. The 

piece of money then seems to be situated atm' n'. 

For the same reason, a pond or river always appears of 
less than its real depth, and a fish is not seen in its true 

688. Refraction by the Air. The air constantly increas- 
es in density from its outer limits to the surface of the 
earth. Hence the effect upon the 
light is the same as though it con- 
sisted of a series of concentric layers 
of different media. As the light reach- 
es each one of these, it is refracted 
Fig. 222. towards the perpendicular and bent 

downward. But the heavenly body, the Sun for example, 
appears in the direction of the last portion of the ray 
which reaches the observer at 0. So the heavenly bodies 
are always seen a little above their true position, except 
when in the zenith. The body S appears at S', Fig. 222, 
and A which is below the horizon appears coming into 
view at A'. 

689. Total Reflection. Since 
when a ray of light passes to a me- 
dium of less density than that in 
which it is moving, it is refracted 
from the perpendicular, the angle 
Fig> jj« of refraction must reach 90°, or 

MIKAGE. 197 

the surface of the refracting medium, before the angle of 
incidence. The ray of light then moves parallel to that 
surface, as c c', Fig. 223. The angle of incidence at which 
this occurs is the Critical Angle. From water to air it is 
48° 35'. 

The angle of incidence can still increase, and by the 
law of sines, the angle of refraction must now exceed 90°, 
or the refracted ray must pass within the surface. This 
is Total Reflection, and the ray obeys the laws of reflection. 

690. Mirage. A phenomenon sometimes seen in sandy desert 
regions, called Mirage, results from refraction and total reflection. 
Fig. 224. The heated sand expands the lower layers of the air and 
makes them less dense than those above. Hence the light pro- 
ceeding from a distant object, as a tree, is refracted upward by 
the successive layers of air. At a certain point O, it reaches the 

Fig. 224* 
critical angle and is totally reflected. The ray then reaches the 
eye of the observer, who sees the object in the direction in which 
the light is moving when it reaches his eye. The object is there- 
fore inverted, and appears as though reflected by distant water. 

The above explanation accounts for the single inverted 
image only. When two or more images are seen, they 
may be accounted for by supposing that at some particular 
distance from the earth's surface, the air has a density 
greater than either above or below. Then rays which pass 



upward would be refracted aud bont downward until they 
reach the observer's eye, so giving an erect image above 
the object. ther rays which pass downward would be bent 
upward, so curving around until they reach the eye, and 
these having crossed each other would form an inverted 
image below the object. Total reflection may occur in 
either case, or the refraction may bend the rays so that they 
reach the eye without total reflection. 

691. Refraction by Traversing Media. Parallel Faces. 
When light passes obliquely through a denser medium 
with parallel faces, it is refracted towards the perpendicular 
where it enters the medium, and away from the perpen- 
dicular where it emerges. This produces a displacement of 
the ray, but its direction is unchanged. 

Thus the ray SQ, fig, 225, which meets 
the section of a glass window pane MN at 
is refracted towards the perpendicular, and 
crosses in the direction OP. At P, it is re- 
fracted from the perpendicular, in the di- 
rection PE, in which the object is seen. So 
the ray appears to come from S', and the 
object is moved, though the direction of the 
ray remains the same. 


Fig. 225. 

692. Prism. A medium bounded by 
planes which are not parallel is called a 
prism. It is usually made so that its sec- 
tion is an equilat- 
eral triangle. Fig. 
226 is a prism. 

ig. 226. 

Displacement by a Prism. An ob- 
ject seen through a prism is moved from 
its true position, and its direction is 
changed. Fig. 227. The ray La from 
the object L is refracted towards the 
Fis:. 227. ^ ase a f t jj e p^ sm n n t a so flj^ | t 

crosses in the direction ah. At h the refraction from the perpen- 
dicular bends the ray once more in the same direction, so that it 



enters the eye at c. The object then appears to be situated at r, 
as shown by tracing back the last part of the ray. 

694. The Solar Spectrum. If a prism be placed in the 
path of a beam of sunlight admitted to a dark room, the 
light is refracted to a new position. But in place of a nar- 
row beam of white light, it is spread out into a number of 
various colors, Fig. 228, which shade into each other. Seven 

Fig. 228. 

colors are usually distinguished, which arranged in the 
order of their refrangibility are Violet, Indigo, Blue. Green, 
Yellow, Orange and Red. These do not include all the 
colors, but only such as are recognized. The spectrum 
really extends a certain distance beyond both ends of the 
visible portion. 

695. These Colors are Simple. This is proved by placing 
a second prism in the path of any one of the colors : the 
light is still farther displaced, but its color is unchanged. 
So by constantly displacing the light by a series of prisms, 
the light can be so extended as to become too faint to be 
recognized by the eye, but so long as it can be seen, it re- 
mains of the same color. 

696. Recomposition of White Light. The above analy- 
sis of sunlight can be proved in a variety of ways. Thus, 
if the spectrum be projected upon a second prism whose 

200 OPTICS. 

base is in the position of the edge of the first, the light 
which passes through is again white. Or the spectrum 
reflected to a focus by a concave mirror gives a white light. 

Newton's Disc. The easiest proof of 
the composition of white light is Newton's 
Disc, Fig. 229. This is a piece of cardboard 
upon which are painted the seven colors as 
nearly as possible in the proportion in which 
they appear in the spectrum. Placing this 
upon a stand and revolving it rapidly, it ap- 
pears white. 

697. Color of Bodies. The color of 
bodies depends upon the light which 
Fig. 229. they reflect. Those which reflect no 

light are black, while those which reflect all are white, pro- 
vided white light illuminates them. No body, however, 
can reflect any light except such as illuminates it. If vel- 
vet of different colors be placed in the solar spectrum, each 
piece appears black except when in light of its own color. 
The reason is that no light is reflected, but all is absorbed. 
So a body in ordinary light appears of any particular color, 
as red, because the light which it reflects makes that im- 
pression upon the eye, while all the other colors are ab- 

698. Mixed Colors. A modification of Newton's Disc 
shows the effect of mixing different colors. If discs are 
used upon which different colors are painted in sections, 
any color can be produced by va^ing the color and dimen- 
sions of the sections. The light from each color falls upon 
the eye, and in place of producing its own sensation, the 
sensations of all combine to produce a new color. So the 
artist produces any tint he desires by mixing his pigments. 

699. Complementary Colors. Colors which united pro- 
duce white are called Complementary Colors. Such colors 
are separated by about half the lenglh of the spectrum. 



Thus red and greenish yellow are complementary: yellow 
and indigo blue, etc. 

If the eye looks for some time intently upon one of two 
complementary colors, the effect upon the retina of the 
eye is such that upon turning away and looking upon a 
white surface, the other appears. Such cases are called ac- 
cidental colors. 

When complementary colors are placed side by side, 
they heighten each other's effects. Hence the most effect- 
ive arrangement of a shop window is to place cloths in it 
according to the complementary colors. So too, articles 
of clothing should be so selected that the colors contrast. 

700. Lenses. These are transparent media bounded by 
curved surfaces. They change the relative direction of 
the rays of light, and they may be divided into two classes 
according to their effects upon light, Convex and Concave. 

701. Convex Lenses bring parallel rays to a focus, as 

A, B, and C, Fig. 230, and are thick- 
er in the middle than at the edges. 

Concave Lenses make parallel 
rays divergent, and are thicker at 
the edges than in the middle, as D, 
E, and F, Fig. 230. 

702. Foci of Convex Lenses. Only 
the double convex need be consid- 
ered, as the others produce similar 
effects, but at greater distances. 
Fi^ 230. Double convex lenses usually have 

sections of spheres for their surfaces. Hence the centre 
of curvature of a double convex lens is the centre of the 
sphere, and the radii are perpendicular to the surface. 

703. Axes. The line joining the two centres of curva- 
ture is the Principal Axis, and Secondary Axes pass 

202 HEAT. 

through the centre of the lens itself, called the Optical Centre. 

704. Focus of Parallel Rays. The focus of parallel rays, 
called the Principal Focus, is found by drawing perpen- 
diculars to the surface, and tracing the direction of the rajs 
through the glass. 

Thus the ray L, Fig. 231, meets the lens at B. Draw FB, the 
perpendicular to the point. The ray is refracted towards that 

Fig. 231. 

perpendicular, and crosses to D. CD is the perpendicular to that 
point, and the emergent ray is refracted from the perpendicular, 
and reaches the focus at F. If the lens is of crown glass, this point 
coincides with the centre of curvature. 

705. Conjugate Foci. If the source of light be at a 
point nearer the lens than an infinite distance, so that th^ 
rays of light diverge, the focus is moved further away. 

Thus if the light 
be placed at L, the 
focus will be at 1. 
These points are con- 
| jugate foci, for each 
is the focus of a light 
placed at the other. 

Fig. 232. The foci of con- 

vex lenses are real, for if a screen be placed at these points, 
it is brightly illuminated. 

The light from a source placed at the principal focus 
becomes parallel rays by the refraction of the lens. 

706. Formation of Images. Two cases demand atten- 
tion : I. Wlmfthe Object is beyond the Principal Focus- 



II. When the Object is nearer the Lens than the Principal 
Focus. When it is at the Principal Focus, the rays become 
parallel, and no image is formed. 

707. 1. Image of an Object beyond the Principal Focus. 

The image is determined by finding two points, the extrem- 
ities, as in mirrors. 

Fig. 233. 

Draw secondary axes from the points, AX and BY, Fig. 233, 
through O, the optical center of the lens. The ray Ar from the 
point A is refracted towards the perpendicular, DF, when it enters 
the lens, and upon emerging, from the perpendicular CE, so that 
it reaches the secondary axis at A' . So any other ray from the 
point A will be refracted to A'. That is all the rays from A will 
then be brought to a focus and form the image of the point A. 
In the same way, the point B is found at B'. The image is then 
beyond the principal focus F, is inverted, real and diminished* 
This may be reversed, that is the object may be placed at A'B\ 
where the image now is. Then the image will be at AB, enlarged. 
This is the principle of Lantern projections. 

708. II. The Object nearer the Lens than the Principal 
Focus. The secondary axes, AX and BY, Fig. 234, now 

meet the rays of 
light on the same 
side of the lens 
as the object. 
The path of the 
rays can now be 
traced as in the 
preceding case, 

Fig. 234. 

♦The principle of the telescope, Sec. 719. 



and they will meet the axes at A' and B\ The image is 
now on the same side of the lens as the object, is direct, en- 
larged, but virtual* 

709. Foci of Concave Lenses. Concave lenses give only 
virtual foci. 

Fofcus of Parallel Rays. The focus is found as with 
convex lenses, by drawing the perpendiculars and tracing 

the rays. 

Thus in Fig. 235, the incident ray- 
SI is first retracted to G and thence 
in the direction GH. So the ray 
S' K takes the direction MN, so 
placing the focus at the point where 
these rays traced back meet the 
principal axis, at F, about half way 
between the centre of curvature C» 

and the lens. This focus is virtual. 

710. If the rays proceed from 
any point, as L, Pig. 236, the 
refracted rays become more di- 
vergent, so that the focus is at 
I. This point is between the lens 
and the principal focus, and this Fig. 236. 

focus is also virtual, while the luminous point and the 
focus are much nearer than before. 

Fig. 237. 

711. Images by Concave Lenses. 

If an object be placed in front 
of a double concave lens, the 
rays will be divergent after re- 
fraction. The required points 
are found by drawing the axes, 
AO and BO, Fig. 237, and trac- 
ing rays until they meet these 
axes. Then the point A is 
found at a, and B at b. 

*The principle of the microscope, Sec. 722 



Hence the image is diminished, is direct, and is virtual. 

712. Aberration. Spherical mirrors and lenses must be 
small, not exceeding 10° or 12°, else the external rays will 
come to a focus before those near the middle. This pre- 
vents a sharply defined focus, lengthening it in the direc- 
tion of the axis, and is called aberration. There are two 
kinds, Spherical, and Chromatic. 

Thus in Fig. 238, the rays near 
the middle of the lens VW have 
their focus at F ; those near the 
edge, at G. 

This crossing of the rays 

is Spherical Aberration. It 

Fig. 238. may be partly overcome by 

covering the lens or mirror so as to use only the central 

portion, but no device has yet been found by which it can 

be entirely removed. 

713. Caustic Curves. When light is 
reflected from the inside of a cylindrical 
mirror, it produces a double curve of light, 
with darker spaces between, Fig. 239. 
These are caustic curves, and are well 
shown by placing a polished silver napkin 
ring upon a table in a beam of light. They 
result from Spherical Aberration, because 

the rays whose angle of incidence is the largest reach a 

focus nearest the mirror. 

Fig. 239. 

714. Chromatic Aberration. A lens is really a prism of 
an infinite number of sides. Hence it decomposes white 
light like a prism, and brings the violet rays to a focus 
nearer the lens than the less refrangible rays, like the red. 
This produces a series of colored rings when a screen is 
placed at the focus, and is called Chromatic Aberration. 



715, The effects of Chromatic Aberration may be over- 
come by using an Achromatic Lens, Fig. 240. 
This consists of a concave lens, A, of flint glass, 
and a convex lens, B, of crown glass. The dis- 
persing power of the flint glass is greater than 
that of the crown glass, so that it neutralizes 
the dispersion while the refraction remains, 
Fig. 240. an( * tne light which has traversed both is white. 
Such lenses are used in all accurate optical instruments. 



716. Some of the more important optical instruments, 
which depend upon the principles already considered, are 
here described. They consist of combinations of prisms, 
lenses, and mirrors. 

Section I. — The Telescope. 

717. Telescopes are of two general kinds, Reflecting and 
Refracting. The latter alone are used for terrestrial ob- 
servations, and most frequently hi Observatories. 

Fig. 241. 
718. A Reflecting Telescope consists of a mirror M, Fig. 241, of 
metal or of glass faced with metal, and an eye piece, O, usually 


a convex lens. Such telescopes are made in a variety of forms. 
The figure gives the form adopted by Sir William Hershel. The 
mirror M collects the parallel rays and converges them to a focus 
at a point between it and the eye piece. They cross and form an 
inverted but diminished image at ab, nearer the eye piece than its 
focus. The lens then enlarges this, so that it appears as a virtual 
image at a'b'. 

The largest telescope in existence, that of the late Lord 
Rosse, is made after this pattern. So also is the magnifi- 
cent instrument belonging to Mr. A. A. Common, at Eal- 
ing, England. This last, which is probably the most 
powerful telescope in the world, has a reflector of glass 
coated with silver, thirty seven and a half inches in diam- 
eter, and a focal length of about twenty feet. 

719. A Refracting Telescope, Fig. 242, consists of a convex lens, 
M, called the object or field glass, used to collect the rays of light. 

Fig. 242. 

and an eye piece. Both are achromatic in all good instruments. 
The object glass forms an inverted, diminished image between its 
principal focus and the eye piece, but much brighter than the ob- 
ject itself. The eye piece N then maguifies this image and makes 
it appear of the dimentions of a b' . Hence the astronomical tele-' 
ssope inverts all objects. This is no real disadvantage, as all are 
inverted alike. 

Very large and fine instruments have been constructed 
upon this plan. That in the Naval Observatory at Wash- 
ington, with an aperture of twenty-six inches is one of the 

720. The Terestial Telescope, Fig. 243, has two additional lenses.* 

♦Sometimes three are used, two doing the work of one 



The first, P, near the object glass, serves to make the rays of light 
which proceed from each point parallel to each other. This makes 
the rays which proceed from the upper part of the object cross 

Fig. 243. 

those proceeding from the lower part at a point H, midway between 
this lens and the next, Q. The second lens brings the rays of 
light from each part to a focus once more at a' b', thus placing this 
image in the same position as the object. This image is then mag- 
nified by the eye piece E, as in the celestial telescope. 

721. The Opera Glass, called also Galileo's telescope, Fig. 244, 
consists of a convex object glass, MN, and a concave eye piece EF. 
The object glass would form an inverted image at a' 6'. But the 

Fig. 244. 

concave lens is placed in the path of the rays just before they 
reach a focus, and causes them to diverge. The eye then sees a 
magnified vertual image at a'b' '. This is erect. 

All telescope lenses are enclosed in a tube blackened 
inside to cut off all light except that from the object under 

Section II.— The Microscope. 

722. The Microscope is either Simple or Compound, ac- 
cording to the number of lenses employed. 

The Simple Miscroscope, Fig. 245, consists of a single 
convex leni M. The object, AB, is placed nearer the lens 



than the princi- 
pal focus, F, so 
that the eye sees 
an erect virtual 
image of the ob- 
ject at A'B'. This 
is much enlarged. 
Its position is 
found by tracing the rays which enter the eye back until they 
meet the axis drawn through the point where they arise. 
Reading glasses are simple microscopes. 

723. The Compound Microscope, Fig. 246, consists of two lenses, 
an object glass M, of very short focal length, and an eye piece N. 
The object AB is placed between the lens M nnd its principal focus. 

Fig. 246. 

The rays, after refraction by the lens, cross beyond it and form an 
inverted magnified image at ab. This is then further magnified 
by the eye piece N, so forming the virtual image at a'b' . 

The lenses of the microscope should be achromatic. 
Besides, for convenience, both object glass and eye piece 
usually consist of several lenses placed a little distance 
apart. This partially overcomes spherical aberration. 
The outer edge of the lens is also covered by a diaphragm 
so as to use only the central portion, for the same reason. 
The lenses are placed inside a tube bLackened to absorb 
all stray rays of light. The tube is also constructed so 
that one part can move inside the other to vary the dis- 
tance between the two lenses, and the distance of the stage 
upon which the object is placed from the object glass can 
also be varied to make the focus exact. 

N, P. 14. 

210 OPTICS. 

Fig. 247 shows the instrument mounted and ready for use, 

Fig. 247. 

with a concave mirror below to condense the light upon 
the object placed upon the stage. 

Section III. — The Camera and Lantern. 

724. The Camera. If a small aperture be made in the 
side of a closed apartment, the objects in front form an in- 
verted image upon the opposite wall.* 

This effect is increased by enlarging 

the aperture and inserting a lens, L, Fig. 

248, in the aperture, because it collects 

more rays of light. The image may be 

allowed to fall upon the opposite wall, or 

Fig. 248. a screen may be placed at the proper 

focal distance of the lens S. The image formed upon the screen 

is always inverted. This forms the Camera. 

725. The Draughtsman's Camera adds a mirror placed at 
an angle of 45°. This reflects the light and forms an im- 
age upon a sheet of paper placed in the bottom of the box. 

726. The photographer uses the Camera, the plate upon 

♦See Section C58. 


which the picture is taken being placed in the focus of the 
lens. The picture is rendered permanent by coating the 
plate with a salt of silver which is decomposed by the light. 
That which is not decomposed is then removed, leaving a 
picture of the objects in front of the instrument. The 
lens is usually made in two parts, as in the microscope. 

727. The Magic Lantern consists essentially of a powerful con- 
vex lens, Fig. 249, placed in front of a strong light, and a lens to 

Fig. 249. 

bring tlie light to a focus upon the screen. The picture, which 
must be transparent, is placed in the slit between the lenses, very 
near the condenser, which simply concentrates the light upon the 
picture. The rays then cross, when they are received by the pro- 
jecting lens and an inverted magnified image is produced upon 
the screen. 

728. Dissolving Yiews are produced by two lanterns 
which project the images upon the same screen. The light 
of one is gradually removed, and that of the other increased. 
This makes one image fade into another. 

729. ^The Solar Microscope. Frequently a second or 
microscope lens is attached to the condenser of the lau- 
tern, and a much smaller projecting lens is then used. 
Using this modification, very small objects can be shown. 
If sunlight is reflected through such an instrument, it \>e-. 
comes a Solar Microscope. 




The light used in a small lantern is a simple kerosene 
lamp. But for use in large halls, the Calcium Light, made 
by placing a stick of lime in the flame of burning oxygen 
and hydrogen mixed, is employed. Sometimes also the 
Electric Light is used.* 

Section IV. — The Spectroscope. 

730. The spectroscope is of special interest because it 
has furnished wonderful information respecting the con- 
stitution of the heavenly bodies. Fig. 250 shows the prin- 
ciple of the instrument, and Fig. 251 shows it mounted 

and ready for use, but omitting the measuring telescope, 
with its millimetre scale. It depends upon the unequal 
refrangibility of different colored light.f 

The spectroscope consists of a prism, P, to produce the spec- 
trum, a telescope, A, through which the spectrum is Viewed, so 
enlarged that only a small part of it is in the field of view at once, 
though by turning A around P 5 all parts can be examined succes- 
sively, and, a telescope B to concentrate the light upon the prism, 

*See Sections 907. 

jSee Solar Spectrum, Sec. G94. 



so rendering the spectrum more intense. A third telescope C is 
usually added, placed so that the prism reflects the light coming 

Fig. 251. 

through this to the telescope A. This carries a small scale divided 
into millimetres, so that the observer can measure the exact 
position of any color of the spectrum. 

731. Each substance when made the source of light, as 
by dipping a platinum wire into some of it powdered or 
dissolved in water, and placing the wire in the flame of a 
Bunsen burner at G, gives a spectrum of certain lines. Thus 
the metal sodium gives a peculiar yellow line that is al- 
ways refracted to a particular place in the spectrum, called 
the D line. To do this however, the light must be allowed 
to enter the instrument by a narrow vertical slit. 

The Spectroscope has furnished a new means of deter- 
mining the presence of the chemical elements, and one 
which recognizes smaller quantities than any other known 
method. It has thus shown some elements to be very 
widely distributed, and has also revealed the existence of 
several elements previously unknown, as caesium, rubidium, 
thallium, and gallium. 

214 OPTICS. 

one source is allowed to pass through a second source giv- 
ing the same color, but which is at a lower temperature 
than the first, the spectroscope shows a dark line where 
the bright line was previously found. That is, the second 
source of light has absorbed all the light from the first. 
Properly, it is a case of interference, or of absorption 
resembling interference, the waves from one source neu- 
tralizing those from the other.* 

When sunlight is thus allowed to enter the spectroscope, 
the spectrum is found to be crossed by a great number of 
dark lines. The position of many of these has been deter- 
mined, and found to coincide with the bright lines of 
known elements. That is, many of the substances which 
are familiar upon the earth also exist in the sun. But 
there, they are in the state of incandescent gas. 

In a similar way, by examining the light of the stars, 
the known substances which exist in them are readily deter- 

Section" 5. — The Rainbow. 

733. One of the effects of refraction, which closely re- 
sembles the previously mentioned optical instruments, is 
the rainbow. It is seen only when the sun is near the 
horizon, and then appears upon the clouds opposite. It 
results from the difference of refrangibility of the different 
colors, joined with total reflection, raindrops acting as the 
refracting medium. To see a rainbow, the eye of the ob- 
server, the centre of the curve of which the arch forms a 
part, and the sun must make a straight line. Hence it can 
only be seen when the sun is near the horizon, for at other 
times the bow is too low to be seen. 

734. The Primary Bow appears with the red upper- 
most, and the violet Lelow. 

*See Interference of Waves, Sec. 385. 



Fig. 252 shows the path of 
the rays which produce it. 
Coming from the sun, they 
are all parallel, and upon 
escaping, only one ray from 
each drop can reach the eye. 
The ray enters the drop at 
the upper part, and is refrac- 
ted towards the perpendicu- 
lar, or downward. It then 
Fig. 252. traverses the drop, and is 

reflected from the opposite side. Upon emerging at the side 
where it entered, it is refracted upward, and reaches the eye. So 
as many drops are required as there are colors, and they must be 
continually falling 

735. The Secondary Bow is above the primary, shows 
the colors in reverse order, and is less brilliant. 

The light which forms this bow enters the 
lower part of the drop A, Fig. 253, is refracted 
upward to B, is then reflected to D, and thence 
to F, where it emerges. Hence the light under- 
goes two reflections, and at each, some of the 
light emerges, because it has not reached the 
Fig. 253. critical angle. 

Section VI.— The Eye.* 

736. The Eye consists of a firm outer coating, shown as 
white in Fig. 254, to keep the eye in its proper globular 

Fig. 254. 

form. Inside of this is a dark coating, the heavy black 
line, which absorbs all li^ht that does not assist in forming 

*The eye is here considered only as an optical instrument: for full discus- 
sion, consult some good Physiology. 



the image. Inside of all is the retina, an expansion of the 
optic nerve, upon which the image is formed, and which 
conveys the impression to the brain. The cornea is a trans- 
parent portion forming the front of the eye, and back of 
that is the iris, a thin curtain with a hole in its central 
portion, which varies its size with the intensity of the light. 
The crystalline lens is a double convex lens placed behind 
the opening. 

An object placed in front of the eye acts as a source of 
light, e. g., the arrow, Fig. 254. The rays then enter the 
pupil through the cornea and the liquid in front of the lens, 
are refracted by the lens and brought to a focus upon the 
retina behind. The image is there diminished and inverted. 

737. Near Sightedness. This defect is caused by too 
great a curvature of the lens of the eye, so that the rays 

of light are brought to a focus 
before reaching the retina, or 
by a lengthening of the body of 
the eye so that the retina is 
thrown behind the focus. The 
model of Fig. 255 shows this by 
slipping the post to the right. 
It is overcome by the use of concave lenses in front of 
the eye. It frequently results from not using due care to 
keep the book perpendicular to the axis of the eye when 

Fig. 23 

Fig. 256. 

Fig. 256, shows a section of an eye in which this defect exists 
The rays of light from the source a are refracted so as to form a 



focus at b, between the lens and retina, -whereas they should focus 
upon the retina at c. 

738. Far Sightedness, illustrated in Fig. 257, is Ihe 
reverse of near sightedness. In this case, from a lack of 
power in the lens, the rays come to a focus behind the 
retina. The remedy for this defect is convex eye glasses. 

Fig. 257. 

Thus in Fig. 257, the rays from the source a are not sufficiently 
refracted by the cornea and lens, so that they reach a focus at b, 
behind the retina, in place of at c, where the retina is situated. 
The result is an imperfect image. 



739. The Undulatory Theory of light has been already 
presented.* Certain peculiar phenomena furnish the 
proof of its correctness and also show that the undulations 
are transmitted. These are Interference, Double Refraction, 
and Polarization. 


740. Fresnel's Experiment, c'tmcmstrates Ihe principle 
of Interference. 

^See Section 144, Page 41. 

+For a discussion of the general phenomena of Inteircrence, see Page 110 
Section 384. 

218 OPTICS. 

Two black glass mirrors, M and N, 
Fig. 258, are attached to each other 
by a hinge s. One, M, is firmly- 
fixed, while the other, N, can be 
moved a little distance forward, and 
is placed so as to make an angle 
varying but little from parallel with 
M. Sunlight is admitted through a 
Fig. 258. screen, concentrated by a lens L, 

to a focus at P, where the rays cross, and then allowed to reach 
the mirrors. The mirror M reflects the rays so that they appear 
to come from the point B, and the mirror N so that they appear 
to come from A. If now a screen X be placed in front of the 
mirrors, the space DF is illuminated by reflection from the mirror 
M, and CE by reflection from the mirror N. These spaces overlap, 
and there is a space DE which receives light reflected from both 
mirrors. This space, in place of being entirely illuminated, is 
crossed by a series of dark lines. Cover either mirror, and the 
lines disappear. That is, light undulations added to similar 
undulations produce darkness. 

This experiment is fully explained by interference, and 
can be explained in no other way. That is, the medium 
which transmits the light is moved in one direction by 
the undulations from one source of light, and in the oppo- 
site by those from the other. One neutralizes the effects 
of the other. 

641. Color of Thin Films. The beautiful colors which 
appear when light is reflected from thin films are produced 
by interference. They are most clearly seen by care- 
fully blowing a soap bubble. When the film of water be- 
comes sufficiently thin, a series of colors appears, the red 
appearing first, and others after that in nearly the order 
of the spectrum. When all have appeared, the central 
part is black. 

The reason for the appearance of these colors is that the 
light reflected from one side of the film interferes with 
that reflected from the other. If the thickness of the film 



is just half the length of a wave of white light, then the 
light from the two sides so interferes as to produce dark- 
ness ; if it is a little more than this, then pale blue appears, 
and so on until the interference produces the color of the 
longest ray, the red. 

742. Newton's Rings. These colors are called Newton's 
Rings, because Newton devised a method of measuring 
the thickness of the film which produces 
^ach color. 

The apparatus for measuring is shown 
complete, in Fig. 259, and in section, to- 
gether with the rings produced, in Fig. 260. 

Fi? 2. 

It consists of a plate of thick glass, P, upon which a plano-con- 
vex lens, L, of very long focus, 
k is pressed. The lens touches the 
plate at one point, which appears 
black in the rings, and the dis- 
tance of the lens from the plate 
Fig. 260. at any point, that is the thickness 

of the film of air at that point, determines the color at that place. 
This is easily calculated 

743. In this way, the length of the undulation which 
produces each color has been determined, for it is twice 
the thickness of the film which appears of that color. The 
red is produced by the longest waves, and the violet by 
the shortest.* 

744. Waves are also found on each side of the colored 
spectrum. Those on one side are too long to produce the 
sensation of sight, while those on the other are too short. 
The waves beyond the violet, however, can cause fluores- 
cence, and most readily produce chemical changes. Sul- 
phate of quinia placed here shines. On the other hand, 

*See Table VIII. 


220 OPTICS. 

a delicate thermometer is most heated beyond the red. 

Fig. 261. 

Fig. 261 shows the comparative intensity of the different 
rays in the different parts of the spectrum. 

745. This last phenomenon suggests the relation be- 
tween heat and light. It shows that they are really one 
force, but that the rays which produce the sensation called 
heat are too long to be seen. 

This phenomenon has often been interpreted as proving 
that a portion only of the rays of the spectrum can be 
properly accounted heat, while others are light, and still 
others, "chemical rays. 17 This interpretation is not true, 
for while sight by the human eye, and the chemical change 
of the silver salts used in photography seem to favor it, 
other salts are more affected in other portions of the spec- 
trum. Besides, there seems to be no good reason for* sup- 
posing that the rays to which our eyes are insensible cannot 
produce sight in other eyes. Color blindness, and the facil- 
ity with which certain animals, notably the cats, can see 
in the night favor this view. 

Section" II. — Double Refraction. 

746. Certain crystals produce a peculiar effect upon a 
ray of transmitted light. The ray which enters as one is 
divided into two distinct rays. One of these, called the 
Ordinary Ray, obeys the laws of refraction : the other, called 
the Extraordinary Ray, is independent of these laws. 



747. Iceland Spar, or crystallized carbonate of lime, 

shows this phenomenon 
very clearly. Fig. 262. 
If such a crystal be placed 
upon a piece of marked 
paper, the mark appears 
double. One of the marks 
seems raised. This is ef- 
rected by the Ordinary 

Fig. 262 

748. Optical Axis. Every double refracting crystal haj 
one line along which the light moves without division. 
This is called the Optical Axis. 

749. Cause of Double Refraction. The explanation of 
Double Refraction is that the light undulations, which are 
retarded to some extent in all directions, are retarded more 
in one direction than in any other. The direction of least 
resistance gives the Ordinary ray: that of greater resistance, 
the Extraordinary. 

Section III. — Polakization. 

750. Closely allied to Double Refraction are the phe- 
nomena of Polarization, since the light which traverses a 
double refracting crystal is polarized. 

Polarized light is light that lias been changed in a pecu- 
culiar manner so as to possess properties different from 
ordinary light. It may be effected by Reflection, or by 
Double Eef raction, and instruments for polarizing the light 
are called polariscopes. They are made in several different 
forms, some doing the work by reflection, others by ref rac- 
tion, and still others combine both methods. 

751. Polarization by Reflection. Place a plane mirror 
of black glass, Fig. 283, so tliat a ray of light meets it ah 



the angle of 35° 25': the light h 
reflected from it, apparently un- 
changed. But if this reflected ray 
is received by a similar mirror 
placed at the angle of 35° 25' with 
the direction of the ray reflected 
from the first mirror, but so ar- 
ranged that it can be turned around 
Fig. 263. £bat ray ^ wnen the secon( l mirror 

is parallel with the first, the light is reflected from the 
second mirror. But when the second mirror is at right 
angles to the first, no light is reflected from it. That is, 
the mirrors have in some way stopped the light. 

752. The action of both mirrors was, in the above exper- 
iment, equal. Half the light was stopped by the first 
mirror, as would appear from measuring the intensity of 
that reflected, and the remainder by the second. The light 
from which half has been removed is called Polarized Light. 

753. The Nichol's Prism is one of the best means of polarizing 

light. It consists of a crystal 
of Iceland Spar carefully cut 
open along the plane joining 
the two oblique edges, AB, Fig. 
264. The two pieces are then 

Fig 264. cemented together by a layer of 

Canada Balsam, and it is mounted in a tube. E is an end view 
of the crystal. 

The layer of balsam totally reflects the Ordinary Ray 
produced by Double Refraction, so sending it to the side 
of the instrument, while the Extraordinary Ray passes di- 
rectly through. The balsam does this because its index of 
refraction is between that of the two rays, the Ordinary 
Ray having a greater index. 

This prism may be used for a polarizer, when half the 
light which enters emerges. But it may also be used for 
an analyser for a ray polarized in any way. 



754. Reason for Polarization. A ray or light may be 
considered as made by transverse movements of the mole- 
cules of the medium in all directions, arid its cross section 
would then be Fig. 265. This by the principle of Compo- 

Fig. 265. Fig. 266. Fig. 267. 

sition of Forces* is the same as in two directions at right 
angles to each other, Fig. 266. Any polarizing instrument 
absorbs those which move in one direction, that is changes 
them to some other kind of motion. The condition of the 
ray is then shown by Fig. 267. The analyzer absorbs those 
moving in the other direction, as it is placed at right angles 
to the polarizerf. 

*\3ee faction 129, page 37. 

+TLc direction in which the waves of polarized light move, whether parallel 
to the face of the polarizer, or at right angles to it awaits determination. 


Part IV. — Electricity. 

755. Introduction. In one form of molecular motion 
the direction of the movement is not fully determined. 
It may be transversal, which would ally it closely to heat 
and light: or it may be longitudinal, which would ally it 
to sound motion: or it may be a union of both movements. 
This movement is called Electricity. 

756. Kinds of Electricity. Electricity appears in sev- 
eral different forms, having special properties, depending 
principally upon the direction in which the movement ad- 
vances, and the manner in which the motion is produced. 
These forms are Magnetism; Frictional Electricity; Cur- 
rent Electricity; and Induced Electricity. 



757. Definition. Magnetism is the force which is mani- 
fested by certain kinds of iron ore, and by pieces of steel 
which have been applied to these, in attracting other pieces 
of iron. It is also manifested by the piece itself taking 
a particular direction, when supported so that it can turn 

Section I. — Magnets. 

758. Natural Magnets are pieces of iron ore that show 
the magnetic force. They are rare, and the name Magne- 


tism is derived from tlie fact that they were originally 
found in Magnesia. 

750. Artificial Magnets are pieces of hardened steel 
which have have been magnetised by any of the methods 
described in Section III.* They are usually made much 
more powerful than natural magnets. They are made 
either as straight bars, called Bar Magnets, or in the form 
of the letter TJ, called Horseshoe Magnets. Artificial mag- 
nets are used for most experiments. 

760. Attraction of Magnets. If a magnet be dipped in 
iron filings, some of the filings are firmly attached. So 
also, if a magnet be brought to a piece of soft iron, the 
iron is attracted. 

761. Poles. A magnet immersed in iron filings attracts 
them principally at the ends, where they are held in large 

quantities. But away from the ends, 
the quantity diminishes, and the mid- 
dle is free from them. Fig. 268. 
Fig. 268. Hence the force is a polar force, or 

is manifested principally at the ends which are called poles. 

The middle is called the neutral line. 

762. Magnetic Curres. If a sheet of stiff' paper be laid 

upon a magnet, and iron 
filings be sifted slowly upon 
it, the filings arrange them- 
selves in regular curves run- 
ning away from the ends of. 
magnet. Fig. 269. The 

Fig. 269. density of the filings gives 

some idea of the intensity of the magnetic force at each 

*See Section 787. 
N. P. 15. 



Names of the Poles. A magnet suspended so as to swing 
freely, comes to rest pointing north and south. The end 
which points towards the north is called the North Pole, and 
the other the South Pole. Imperfect magnets frequently 
have poles between the ends, separated by neutral lines. 
These are Consequent Poles. 

763. Mutual Action of Poles. 

Fig. 270. 

If the north pole of a magnet be 
brought towards the north pole 
of another which is suspended, 
Fig. 270, the suspended magnet 
moves away from the other. 
But if the south pole be pre- 
sented to the north pole, the 
suspended magnet moves to- 
wards the other. 

The same series of exper- 
iments may be repeated at 
the south pole of the sus- 
pended magnet, with corres- 
sponding res nits. Hence the 

Law. Like poles repel each other: unlike attract. 

764. Broken Magnets. If a magnet be injured, it loses 
a portion of its magnetism. But the force can not be en- 
tirely removed by this means. Indeed, no method is known 
for entirely demagnetizing any body which has been once 
magnetized, except by heating it red hot. It can be reduced 
to a very small amount by other means, but not entirely 

If a thin bar magnet be carefully broken, each part 
becomes at once a magnet. The former poles remain un- 
changed, but a new pole has been developed in each piece. 
This shows that the magnetizm is not confined to the ends 
of the magnet, but extends all through it, being manifested 
mainly at the ends. 

765. Magnetic Induction. If a magnet be brought near 



a piece of soft iron, the iron speedily becomes a magnet 
and attracts iron filings. The distance at which the iron 
is affected is called the Magnetic Field. The force is devel- 
oped by the mere presence of the magnet, and while it is 
increased by bringing the magnet and the iron into 
contact, this is not essential. The iron developes 
both poles. This action is called Induction. 

766. Magnetic Chain. If a bar magnet be sus- 
pended, and a piece of soft iron, as a key, Fig. 271, 
be placed in contact with it, the latter becomes a 
magnet by induction. A second piece can now be 
added, and a third to that, and so on, until the 
weight of the pieces exceeds the magnet's strength. 
Fig. 27L This i s called the Magnetic Chain, 

767. Action of Opposite Poles. If two equal magnets be 
placed with the contrary poles together, the action of one 
neutralizes the action of the other. 

This is well shown by laying down a 
bar magnet and attaching to it a piece of 
soft iron, Fig. 272. Now slowly move the 
opposite pole of a second bar magnet 
over the first. Just before it reaches the 
Fig. 272. end? the i ron falls . 

768. Armature. Use increases the strength of a magnet 
up to a certain limit called saturation. So to 
increase its action, or to keep a magnet in con- 
stant use, an Armature or Kejeper is provided, A, 
Fig. 273. This is a piece of soft iron placed 
from pole to pole, and it completes the circuit. 

Fig. 273 shows a Magnetic Battery, consisting of a 
series of thin magnets bound side by side, fitted with 
un armature. Such a battery is much more powerful 
than a single magnet of the same dimensions. 

Fig. 273. An armature is applied to bar magnets by placing 



Fig. 271. 

two side by side with 
their poles in opposite di- 
rections,Fig. 274. Pieces 
of iron are then placed 
from pole to pole. 

769. Theory of Mag- 
netism. The difference 
between a magnetised and an unmagnetised bar is not 
fully understood. The probable explanation would seem 
to be .connected with the polarization of the molecules. 

770. Ampere's Theory of Magnetism attributes the 
magnetic force to a constant current of electricity passing 
around each molecule of a magnetized bar. These currents 
accumulate at the surface. Hence magnetism is princi- 
pally manifested at the surface. ' 

771. Polarization Illustrated. The molecules of an 
unmagnetized bar may be conceived as 
possessed of polarity, but arranged in 
all directions. Fig. 275. But the bar 
after perfect magnetization consists of 
the same molecules all arranged in a 
definite order. Fig. 276. The north 
pole of the various molecules represented 
by the black portions, at first occupied 
different positions, so that the currents 

neutralized each other. After magnetization, the poles are 
turned in a single direction. 

772. This explanation accounts for the known increase 
in the length of a bar when it is magnetized. So too, when 
a large bar is quickly magnetized, a sharp click is heard. 

773. Upon this view,.the difference between iron and 
steel consists in the ease with which the molecules change 
their position. Iron offers little resistance, and a bar of 
iron is almost instantly magnatized. A bar of steel offers 


Fig. 275. 

Fig. 276. 


considerable resistance to taking the magnetic positions. 
But when it is once polarized, the molecules never regain 
their former positions. 

Section II. — The Magnetic Needle. 

774. When a bar magnet is suspended, it points in 
a single direction, called the Magnetic Meridian. The 
north end is called the North Pole, and the other the South 
Pole. The magnet takes this direction because of the 
directive action of the earth, which acts as a powerful mag- 
net with one pole near its own north pole and the other 
near its south pole. 

775. Magnetic Needle. A very light magnet balanced so 
as to move freely around a point is called a Magnetic Nee- 
dle. Such a needle is shown suspended by a fine cord in 
Fig. 270. It usually makes an angle with the meridian of 
any place, that is, with the true north and south line. The 
angle is called the Declination of the Place. This is east 
or west, according to the side of the meridian. The Decli- 
nation is at present West for the Eastern portion of the 
United States, and East for the Western portion. 

776. Agonic Lines. A line connecting places where 
there is no declination is called an Agonic Line. Such a 
line passes near Detroit. 

777. Variation of Declination. The Agonic Line moves 
gradually Westward, so that the needle at any place seems 
to make oscillations to each side of the meridian. The entire 
period required to complete the oscillation is not fully de- 
termined, but it must require several centuries. This 
change is called the Secular Variation. 

778. Annual and Daily Yariations. There is a small 
variation according to the season of the year. Thus at 
London, the Declination is greatest about March 20th, then 



diminishes for about three months, and increases again for 
the rest of the year. This change, however, amounts only 
to about 15'. 

779. There is also a similar change of about the same 
amount which occurs each day. The maximum is about 
two p. m., and the minimum about four a. m., though 
there is very little change after ten p. m. This change is 
the Diurnal Variation. 

780. Compass. The compass is simply a magnetic needle 
suspended in a graduated box. It is of two kinds, the 
Surveyor's Compass, and the Mariner's, 

781. The Surveyor's Compass consists of a brass case 
accurately divided into degrees, with a needle turning just 
inside the graduated circle. Sights, consisting of pieces 
of brass with very narrow holes in them, are placed across 
the zero line, or the north and south line of .the instru- 
ment. A telescope is frequently placed above the needle, 
when the instrument becomes the Surveyor's Transit. 

782. The Mariner's Compass, Fig. 277, has a card at- 
tached to the needle 
and moving with it. 
This card is divided 
into thirty-two 
points called 
Rhombs, and a 
mark is made on 
the box in the di- 
rection of the keel 
of the ship, so that 
the instrument 
points to zero when 

Fig. 277. the ship sails due 

north. The compass is suspended upon gimbals, which 
permit of motion in two directions at right angles. This 



keeps the compass uniformly horizontal.* The needle is 
balanced before magnetization, and a light movable 
weight is attached to overcome the effects of Inclination 
and keep the needle uniformly horizontal. This is essen- 
tial to delicacy. 

783. The Dipping Needle. If a carefully balanced nee- 
dle be magnetised, it 
no longer remains hor- 
izontal, but the north 
pole descends. This 
is called the Inclina- 
tion, or Dip of the nee- 
dle. A needle care- 
full y balanced and 
free to turn upon a 
horizontal axis, and 
then magnetised, is 
called a Dipping Nee- 
dle, Fig. 278. 

Fig. 278. 

784. If a dipping needle be placed at right angles to the 
magnetic meridian, it stands vertical. Placed in the me- 
ridian, by turning it around a vertical axis through exactly 
90°, it stands at an angle called the Inclination of the" 
place. At Greenwich, it is about 67°. 

785. Magnetic Poles. The places where the Inclination 
is 90°, or the Dipping needle is vertical, are called Mag- 
netic Poles. The north pole, where the north end is 
downward, was found in 1830 by Sir James Ross. It is 
near Baffin's Bay, in Latitude 70° N., and Longitude 96° 
43' W. The south pole, where the needle stands vertical 
with the south pole downward, has never been found. 

786. Magnetic Equator. Places where there is no dip, 

*In the best form, as made by Messrs. Kitchie of Boston, the needle floats 
in liquid also. 


or where the needle is horizontal, are said to be on the 
Magnetic Equator. A line connecting such places forms 
an irregular curve, varying from a great circle of the earth 
by being in some places north of it, and in others south. 

787. Astatic Needle. A needle which is not acted upon 
by the earth is called Astatic. A needle may be made 
astatic by placing magnets around it until it remains in 
any position in which it may be placed. 

An Astatic System consists of two equal 
magnetic needles firmly attached by copper or 
silver wire, Fig. 279. The north pole of one is 
above the south pole of the other. This ar- 
rangement is used in delicate galvanometers.* 
When perfect, and suspended by a fiber of un- 
Fig. 279. twisted silk, such a system points east and west. 

Section III. — Methods of Magnetization. 

788. Sources of Magnetism. Magnetism may be pro- 
duced by the Influence from other Mac/nets; by Induction 
from the Earth; and by Currents of Electricity. 

Magnets may be applied in either of three ways called 
Single Touch, Separate Touch, and Double Touch. 

789. Single Touch. To magnetize a bar by this method, 
the pole of a magnet is placed upon one end of the bar, 
and slowly moved to the opposite end! It is then removed 
and returned to the starting point. This is repeated 
several times, always in the same direction. Feeble mag- 
nets are provided in this way, but they are fine needles, as 
they are usually free from all consequent poles.* The end 
touched last has opposite polarity to the pole which 
touches it. 

*See Section 893. 
tSee Section 7G2. 


790. Separate Touch, consists in placing the opposite poles of 
equal magnets upon the middle of the bar to be magnetized, and 

moving them slow- 
JL^ ^J«U *y a P art - They are 

then replaced, and 
the operation re- 
peated. After sev- 
Fig. 280. eral movements, 

the bar is magnetised. The operation may be performed quicker, 
and stronger magnets may be produced, by placing the bar to be 
magnetised upon the opposite poles of two bar magnets, Fig. 280, 
and inclining the magnets moved at an angle of about 45°. 

791. Double Touch. In this method, the bar to be mag- 
netised is supported as in Fig. 280, and the two poles of a 
horse shoe magnet are placed in the middle. They are 
then moved to one end, and back again ; then to the other, 
and back; and so on, care being taken to move them the 
same number of times to each end. The magnet is finally 
removed from the middle. Powerful magnets are pro- 
duced by this method. 

792. Induction by the Earth. If a bar of iron which is 
not quite pure be placed in the position of the dipping 
needle and struck or twisted, it becomes a feeble magnet, 
and will retain its magnetism for a time. So too such 
tools as remain standing for a long time in nearly this 
position become feebly magnetised. 

In like manner, iron turnings are often found magnet- 
ised. In all these cases, the magnetism results from 
induction, and the north pole is downward, in latitude 
north of the equator. 

Iron ships, being hammered in building, become mag- 
netic. This too is produced by induction, and the direc- 
tion of the ship's poles depends upon the position of the 
keel upon the stocks. 

793. Magnetization by Electricity. The most powerful 
magnets are very quickly made by charging with an elec- 



tro-magnet.* The bar to be magnetised is simply made 
an armature, and if the power of the electro-magnet is not 
too great, the bar is moved back and forth two or three 
times upon the poles. This quickly magnetises the bar to 



794:. Frictional Electricity is so named because the most 
convenient method of developing the force is by using 
friction. It is also called Static Electricity because of its 
great power to overcome resistance. 

Section I. — Fundamental Phenomena. 

795. If a warm dry glass tube be rubbed with silk, it 
attracts light bodies placed near it. This is well shown by 
bringing such a tube near a quantity of bran, when the 
bran moves to the tube, remains in contact for a moment, 
and then moves away. 

Fig. 281. 

In a similar way, if the excited tube be brought near a pith ball 

*See Section 896. 


suspended by a thread, the ball moves towards the tube, touches 
it, remains in contact a moment, and retires. Fig. 281. 

A beautiful way of showing this attraction is to excite a 
large tube very highly and hold it out towards an empty 
egg shell; the shell will roll after the tube. 

796. Polarity. A suspended pith ball is called an 
electric pendulum. After it has touched the excited glass 
tube, it is repelled. Fig. 281. But excite electricity in a 
stick of rubber or sealing-wax by rubbing with dry flan- 
nel, and it will attract the excited pith ball. 

Allow the excited pith ball to touch the sealing-wax, 
and it remains in contact a moment, and is then repelled. 
If both the tube and the sealing-wax are held towards it, 
the ball will vibrate back and forth between them. Hence 
there are two kinds of electricity, Positive and Negative, 
marked + and — . 

797. The electricity excited in glass by rubbing with 
silk is made the starting point, and all bodies which repel 
the pith ball which has been electrified by contact with 
the excited glass are said to be + electrified. All those 
which attract the pith ball are said to be — . Which kind 
of electricity will be developed in any particular substance 
by friction from another substance can only be determined 
by experiment. 

798. Both electricities are simultaneously developed, 
and in equal quantities. This can be shown by hanging 
up the silk which is used as a rubber, and then rubbing it 
with the glass tube. It then shows the electricity which 
formerly escaped through the hand. 

799. Conductors and Non-Conductors. Certain sub- 
stances, especially glass and the resins, retain electricity in 
the parts where it is developed. These are called Non-Con- 
ductors. Others offer very little resistance to its passage 
from point to point. The metals are the best illustrations 
of this class of substannces. Thus if a l>ar of iron be held 


by a glass handle and struck with flannel or cat's skin, 
electricty is developed. But it is manifested in all parts 
of the bar with equal intensity, while if a glass tube be 
rubbed, the electricity appears only in the part rubbed. 
Bodies which allow electricity to move freely from part to 
part are called Conductors* 

800. Insulation. A body which is surrounded by bad 
conductors is insulated. Since dry air is one of the poorest 
conductors known, all that is required to insulate a body 
is to prevent the passage of electricity to the earth. This 
is usually effected by supporting the body upon glass. 
Since glass is quite hygroscopic,! its insulation is improved 
by varnishing it with shellac. 

801. Detection of Electricity. To detect small quantities 
of electricity, electroscopes are used. The electric pen- 
dulum is a simple electroscope. 

802. The Gold-Leaf Electroscope, Fig. 282, is one of the most 
delicate arrangements for discovering the presence of 
electricity. It consists of a glass jar fitted with a metal 
cap. A brass rod terminated by a ball at the top passes 
through this, and two small strips of gold-leaf are at- 
tached to its lower end. Two strips of tin-foil commu- 
nicating with the earth are sometimes pasted to the 
inside of the glass, to prevent such a charge as would 
injure the gold-leaf. When the charge becomes excessive, , 
the leaves touch the tinfoil, and are discharged. 

282. ij> prevent injury to the instrument, the proof 
plane, a small disk of metal attached to a glass handle, is 
used to transfer a minute quantity of electricity from the 
body under examination. 

803. Induction on the Electroscope. Sometimes the 

*For the table of Conductors and Non-Conductors, or of Electrics and Non- 
Electrics, see Table VII. 
tThat is, condenses moisture from the air upon its surface freely. 
J See Sections 795 and 70ft. 



electroscope is charged by Induction* This is done by- 
bringing the body to be examined near the ball of the elec- 
troscope: the leaves diverge. The ball is then touched by 
the finger, when the leaves collapse. But removing the 
charged body, they diverge again, with the opposite kind 
of electricity to that contained in the body. 

Fig. 283. 

804. Electrometer. The Electrometer is used for 
measuring the quantity of electricity contained in a 
charged body. Fig. 283. It consists of a pith ball 
suspended to the centre of a graduated arc by a piece 
of straw. It is then attached to the body whose 
charge is to be measured, and the pith ball rises along 
the arc with the increasing charge until it stands at 

right angles to the body. 

Section II. — Laws of Electricity. 

805. The Laws of Electricity relate to the Intensity of 
its Attraction and Repulsion: to its Distribution: and to 
its Density at Particular Places. 

806. Coulomb's Torsion Balance is used to determine these laws. 
It consists of a glass case carrying a 
small glass tube, d, Fig. 284, which 
has a brass cap a, at the top, graduated 
to degrees. A fine silver wire is sus- 
pended by this cap and carries a small 
shellac needle, o, at its lower end. 
The needle has a small gilt ball, n, at 
one end, and is carefully balanced. 
A scale of degrees is fixed around the 
inside of the glass case, and opposite 
its zero a small shellac rod,i, is let in, 
and a gilt ball m of the same size as 
the one upon the needle is fixed to its 
lower extremity. 

807. Determination of the 
Laws. The shellac rod is removed 
and its ball charged by contact 
with an electrified body. It is 

Fig. 284. 

*See Section 814. 


then replaced and it touches the ball upon the shellac needle, 
and because it is of the same area, it gives it one half the 
electricity. Since both are now charged with the same 
kind, they repel each other. This turns the needle away 
from the shellac rod through a certain distance, so twisting 
the wire against its elasticity of torsion.* When it comes 
to rest the number of degrees is read. The cap and silver 
wire are now turned until this number of degrees is reduced 
to one-half its original number. The force of torsion is 
then read from the cap in degrees, and found to be four 
times the amount in the former instance. Hence, at one- 
half the distance, the repulsion becomes four times as great. 
The same method may be applied to two bodies electrified 
with opposite electricities, when they will attract each 
other. Hence I. Electrical Attraction and Repulsion vary 
inversely as the square of the distance. This fixes electricity 
as one of the radiant forces. 

808. To determine the effect of varying the charge of 
electricity, the shellac rod is removed and charged as be- 
fore. The needle then removes one-half of the electricity, 
and is repelled a certain number of degrees. The shellac 
rod is then removed and half of its electricity removed by 
touching another sphere of equal size. Upon replacing 
it, the needle is repelled through one-half the number of 
degrees of the previous instance. Hence II. Electrical 
Attraction and Repulsion vary as the product of the quan- 
tities of Electricity. 

809. Position of the Force. An insulated 
brass sphere is fitted with two hemispher- 
ical covers, as shown in Fig. 285. The 
sphere is then charged with electricity, 
and the covers applied by means of glass 
handles. Removing them and applying 
Fig. 285. the gold-leaf Electroscope, they are 

found charged. But apply the Electroscope to the sphere, and no 

*See Section 48, page 13. 


electricity is found in it. Hence the Electricity is distributed on 
the Surface of a Body. 

810, Experimental Confirmation. A hollow insulated 
sphere is charged. Applying the proof plane to the inside 
through a hole in the top, no electricity can be found. But 
electricity can be taken from the outer surface. 

So, if a gauze cylinder be placed upon an insulated metal 
stand and charged, the proof plane again shows that the 
electricity is upon the outer surface.* 

811. Distribution in an Electrified Body. This depends 
upon its shape. In a sphere, the electricity is distributed 
uniformly. But if the body be elongated, that is becomes 

an ellipsoid, the electricity accumulates 
near the ends. 

This is -well shown by the apparatus of Fig. 
286. An elongated ellipsoidal conductor is 
charged with electricity. Applying the proof 
plane to the central portion shows but little 
Fig. 286. electricity. At the large end, it is a little more 

dense. But at the smaller end, it accumulates strongly. 

812. Effect of Points. When the conducting body is 
extremely elongated, the tension of "the electricity exceeds 
the resistance of the air, and it is dissipated. Hence if a 
point be placed upon a conductor, the electricity escapes as 
fast as it is generated. 

Because points allow the escape of electricity, a prime 
conductor is always made with oval ends. It is also highly 
polished, and care is taken that it is free from rust and 
dirt of all kinds, as each particle acts as a point and allows 
the escape of electricitj'. 

813. The effect of a point is well seen in a darkened 
room. The -escaping electricity then appears as lines of 

♦This principle holds only for Frictional Electricity, and for that only when 
Induction is absent. 


light. This produces a peculiar appearance called the spark. 
The form of the spark differs to some extent, depending 
upon the kind of electricity escaping from the point. 
When + escapes, Jhe form is that of a brush: when — , 
it is more rounded and is called the glow. 

Section III. — Induction. 

814:. When an electrified body is brought near an un- 
electrified, but they are separated from each other by a 
non-conducting medium, the latter body becomes electri- 
fied. It, however, contains both kinds of electricity, but in 
different portions. This method of exciting electricity is 
called Induction. 

815. Induction Shown. Place an insulated prime con- 
ductor with pith balls attached to the ends near a + elec- 
trified body, as a glass tube, Fig. 
287. The pith balls diverge. If 
a gold-leaf electroscope charged 
with + electricity be brought 
near the end of the conductor 
from the tube, the leaves di- 

Fig.287. verge still more, showing that 

that end contains + electricity. If the electroscope be 
presented to the middle, no electricity is found. But at 
the end nearest the tube, they diverge less, showing that 
— electricity exists at that end. Hence both hinds of elec- 
tricity are developed by Induction. 

816. Free and Confined Electricity. A portion of the 
conductor in which electricity is induced, between the ends, 
is neutral, that is, contains no electricity. If the end of 
the conductor nearest the charged body be connected 
with the earth, no change is shown by the pith balls. But 
if the end away from the charged body be connected with 
the earth, the pith balls at that end instantly fall. The 


electricity there lias disappeared. The neutral Hue, which 
formerly was at the middle of the iusulated conductor, is 
now removed to an infinite distance. 

If the charged body be now removed, the induced elec- 
tricity spreads over the entire surface of the conductor. 
The pith balls at both ends diverge, but not as far as 

817. Induction, in the experiment given above, acted 
between two bodies separated by a layer of air. It acts 
equally well when the bodies are separated by some other 
non-conductor. Faraday proved this by placing a charged 
ball in the middle of a copper pail while a second copper 
pail was outside of the first and separated from it by a layer 
of shellac. Induced electricity appeared in both. Indeed, 
each non-conducting substance has a definite power of 
its owu for producing induced electricity called its induct- 
ive capacity. 

The essential condition then to produce induction seems 
to be that the two bodies be separated by a non-conducting 
medium. Could they be separated by a perfect vacuum, it 
seems probable tj^at induction would not occur. 

818. Cause of Induction. The real cause of induction is the 
polarization of the molecules of the intervening medium. That is, 
the electrified body acts upon the row 
of molecules next itself, causing one 
side to become + and the other — , as 
shown in Fig. 288, where the circles 
represent molecules whose darkened 
side is +. This first layer then acts 
Fig. 288. upon the next, and so on until the 

other conductor is reached. The last layer polarizes the first 
layer in that, in a similar way. But because it is a good conductor, 
its molecules do not retain the electricity. Each molecule dis- 
charges at least one kind, and those near the middle, both. So 
the attracted electricity all manifests itself near the inducing body, 
while the repelled moves as far away as possible. 
N. P. 16. 


819. Induction Precedes Discharge. In all cases, the 
molecules of the resisting medium are polarized before a 
discharge takes place through it. This explains why elec- 
tricity follows the path of the least resistance. In this 
path, there is the least number of polarized but undischarged 
molecules . 

820. The Electric Pendulum. Induction also explains 
the electric pendulum. As soon as the excited body is 
brought near the suspended pith ball, the ball becomes, 
charged with both kinds of electricity by induction. The 
side of the ball towards the electrified body is attracted, 
and is the nearer half; the other and more distant is re- 
pelled. The attraction exceeds the repulsion, being exert- 
ed through the less distance, so that the ball moves to 
the charged body. - 

All cases of electrical attraction and repulsion are simi- 
lar. But when the attracted body is in contact with the 
earth, one kind of the induced electricity passes to that. 

821. The Condenser. The simple 
instrument as made by Epinus, Fig. 
289, consists of two metal plates, 
marked + and — , separated by a 
plate of glass. The metal plates 
are capable of taking a much greater 
Fig. 289. charge than if used alone. 

822. To charge the condenser, the metal plates are 
placed in contact with the glass, and one of them put in 
connection with a source of electricity, as the prime con- 
ductor of an electrical machine,! while the other plate is 
connected with the earth. The plate in contact with the 
conductor receives from that a certain amount of free elec- 
tricity, so that its tension in^all parts equals the tension 
of the conductor. This free electricity upon the + plate 
acts upon the other plate, through the glass, by induction. 


This develops — electricity upon the side next the glass, 
and repels the + to the earth. If both plates carry pith 
balls, the one attached to the + plate will diverge, while 
the other is unaffected. 

823. Now remove the condenser from the prime con- 
ductor, and break the connection with the earth ; the pith 
balls remain unchanged. But if the plates be removed so 
far from each other that induction ceases to act, the elec- 
tricity is free to spread over both surfaces of the plates 
equally. The pith ball attached to the : — plate now di- 
verges as much as the other did when in contact with the 
glass, while that on the + plate diverges more than be- 
fore, because formerly the inductive action of the — plate 
concentrated electricity upon the surface of the + plate 
nearest itself, and this now becomes free. 

824. To discharge the condenser instantaneously, touch 
the — plate with a conductor, and then bring the other 
end in contact with the + plate. A spark passes. 

It may be discharged slowly by touching first the -h 
plate with a conductor, then the — , and so on alternately. 

825. The Fulminating Pane consists of a plate of 
glass coated on each side with tin-foil to within about two 
inches of the edge. One coating is then brought in con- 
tact with a source of electricity, as a prime conductor, and 
the other connected with the ground. It acts as a con- 

826. The Leyden Jar. The most convenient 
form of the condenser for common use is the 
j Leyden Jar, Fig. 290. It consists of a wide mouthed 
bottle coated inside and out with tin-foil, about 
two-thirds the way up. A cap of baked wood, 
coated with shellac, is fitted to the top, and a wire 
passes through this to the inside coating, and 
M&29oT terminates with a ball at the top. 




827. Charging the Jar. The Jar is charged by connect- 
ing the inside coating with the prime conductor of a Plate 
Electrical Machine,* while the outer coating is connected 
with the earth. If the Holtz Machinef is used, the outer 
coating should be placed in contact with one pole, and the 
inner with the other. 

828. A Leyden Battery, Fig. 291, 
consists of several jars whose coat- 
ings are connected. This is accom- 
plished by placing the jars in a box 
lined with tin-foil, thus connecting 
the outer coatings, and wrapping 
a wire around the rods to connect 
the inner coatings. 

The Leyden Jar acts entirely 
Hence connecting several jars 

Fig. 291. 

by the area of the coatings. 

into a battery only increases the area. 

829. Jar with Movable Coatings. It has already 
been stated that when induction does not act, the 
electricity is entirely upon the surface 4 But when 
induction acts, the result is different. For, charge 
ajar having movable coatings, Fig. 292. Then by 
using a glass handle, remove the inner coating from 
the jar, and the jar from the outer coating. Now 
wrap a sheet of tin-foil around the jar for an outer 
coating, and fill it about two-thirds full of water for 
an inner coating. The jar can now be discharged, 
showing that the charge was in the glass. The 
Fig. 292. cause of this is that each kind of electricity holds 
the other as near to itself as possible. This causes each to pene- 
trate the glass, and prevents it from leaving with the coating. 

830. Residual Discharge. Moreover, the charge of the 
jar does not remain upon the surface of the glass. After 
a strongly charged jar has been discharged, allow it to re- 
main a short time, and a second spark less intense than the 

*See Section 835. 
+See Section 838. 
+See Section 809. 


first can be taken from it. That is, the electricity has 
acted upon the molecules in the interior of the glass, and 
during the short time occupied in discharging the jar, they 
cannot discharge themselves. 

Section" IV. — Production of Electricity. 

831. The usual way of developing large quantities of 
electricity is by means of Electrical Machines. These act 
upon two principles, Friction, and Induction. 


832. The Electrophorus is the sim- 
i plest Electrical Machine. Fig. 293. 
It consists of a metal plate and a cake 
i i 0* of resin* resting upon it. A cover of 
tin with a glass handle to insulate it 
covers the resin to within an inch of the 

The resin is first dried and warmed, 
Fig. 293. an( j then beaten or rubbed with cat's 

skin. This developes — electricity upon the surface of the 
resin. The cover is then placed upon it. The surface of 
the resin, though made as smooth as possible, is really so 
rough that the tin cover touches only a few points, so that 
the resin acts by induction upon the cover. Its under 
surface then becomes + and its upper — : touching the 
upper surface with the finger allows the — to escape. 
Upon raising the cover, the 4- spreads over its entire sur- 
face and becomes free, so that it may be used for any pur- 
pose, as charging a jar. 

833. The Electrophorus acts only by induction, and de- 
pends upon the roughness of the surface of the resin. Me- 
chanical labor is expended in separating the cover from 
the resin for each spark, so that mechanical energy is 

♦Conveniently made of four parts resin and one shellac. 



really changed to electricity. This is the case with all the 

834. Frictional Machines are usually made as Cylinder 
or Plate. The latter only is in common use at present. 

Fig. 294. 

835. The Plate Machine, Fig. 294, consists of a large glass plate 
fixed upon wooden supports, and turned by a crank. A pair of 
leather rubbers, which have been covered with an amalgam of 
murcury, tin and zinc, are made to press upon the plate by a brass 
spring. These rubbers are usually insulated by a glass support, and 
are connected with a brass ball, which is the — conductor. A flap of 
oiled silk extends from the lower side of the rubbers, and a silk bag 
encloses all the lower part of the plate. This prevents the escape 
of electricity into the air. A brass insulated prime conductor 
stands on the opposite side of the plate, and a fork ending in a 
knob extends from this about one third across the plate, having a 
row of points towards the plate. 

836. The friction of the rubbers upon the plate generates 
+ electricity upon the plate, and — upon the rubbers. 
The row of points, called the comb, takes the + from the 


plate and accumulates it in the prime conductor, and the 
plate at the same time acts inductively upon the comb. 
This transfers — from the prime conductor to the plate. 

837. If it is desired to generate any large amount of 
electricity, the — conductor must be connected with the 
ground. This allows the machine to act until the tension 
of the prime conductor equals the resistance of the glass 
plate, when the electricity will leap across from the fork 
to the rubbers.* 

Fig. 295. 

838. Holtz's Electrical Machine, Fig. 295, is far more effective 
than the plate machine, and acts by induction so far as its action 
is understood. It consists of a narrow plate of strong glass 
supported upon wooden pillars. This supports a thin glass plate 
by a shaft, so that it can be revolved rapidly by means of a 
crank and pullies. Beyond the revolving plate and about half an 
inch distant from it is a fixed plate also supported by the plate and 
pillars. Two windows are cut in this fixed plate, on opposite sides 
of a diameter, and pieces of paper, armatures, are pasted upon 
this plate, away from the revolving plate. A row of points ex- 
tends from this into the windows. The armatures and points are 
so arranged that the revolving plate turns towards them. A brass 
conductor, called the cross comb, the ends being covered with 
points, is placed from one armature to the other. The sustaining 

*In using any electrical machine, it must be carefully freed from dust, and 
warmed to prevent any moisture from adhering to the surface of the glass. 
The air must also be dry. 


plate also supports rows of points, called collecting combs, op- 
posite the windows, and each' of these is connected with a Leyden 
Jar, and the poles where the electricity is collected are also con- 
nected with these jars. One pole can be moved by a wooden han- 
dle to lengthen the spark. 

839. The action of the machine is as follows. The 
armature on the side nearest the crank is excited negatively 
by rubbing with cat's skin, or by touching with a — ebon- 
ite plate, and the plate revolved. The excited armature 
acts inductively upon the part of the plate opposite itself 
and makes that + on the face towards itself, and — on the 
other side, and the — goes at once to the conductor, while 
the conductor's + goes to the plate. As soon as this ex- 
cited portion of the plate gets opposite the other armature, 
it acts inductively upon that, making it +, and that in 
turn acts upon the + conductor, taking its — to the plate. 
The revolution of the plate renders this action continuous. 

840. There are many things in the action of the ma- 
chine that the above explanation does not account for, as 
for example, the action of the cross comb, but it is all 
that is at present known . The electricity produced is much 
more intense than that from the Plate Machine. It is also 
much greater in quantity. 

There are many other machines, but all involve the same 
principles as these, or are combinations of both.* 

Section V. — Effects of Electricity. 

841. With any good machine, a large number of exper- 
iments can be performed illustrating the principles devel- 
oped in the preceding sections. 

842. Electrical Repulsion. The electrified head, a doll's 
head covered with hair, or strips of paper, is a fine illus- 

*For a full account, see Ganot's Physics, or Deschanel's Natural Philosophy. 



tratiou of electrical repulsion. As soon as it is placed in 
connection with a source of electricity, the hairs diverge. 

843. Insulating Stool. This is a 
stool with glass legs,* Fig. 296. If a 
person stands upon such a stool and 
touches a prime conductor, he very 
quickly becomes charged with elec- 
tricity. His hair shows the revision, 
and a spark can be taken from any 

Fig. 296. 

part of his body. 

844. The Electric Chime, Fig. 297, acts 
by induction. A series of bells are suspended 
from a glass support and connected with the 
prime conductor of an Electrical Machine. 
The glass support also has a bell which is 
connected with the earth. A series of small 
clappers are supported by silk thread so 
that they can play back and forth between 
the outside bells and the middle one. When 
the machine is worked, the outside bells be- 
come + , act upon the clappers by induc- 
tion, and cause them to move to the bells. 
They are then repelled, and play back and forth between the cen- 
tre and outside bells. 

Fig. 2% 

84:5. Electrical Wind. The effect of a point is well shown 
by a point placed upon the prime conductor. Working 
the machine, a wind is felt by the hand moving from the 
point, caused by the discharge of electricity into the air. 
The flame of a candle is turned away from the point. The 
electricity escapes from the point and electrifies the air 
which moves away because of repulsion. A brush appears 
in a dark room. 

846. The Electrical Whirl, Fig. 298, shows the same 

*Four large bottles of equal size with a square board placed upon them an- 
swer all the purposes of an insulating stool. 


*§§§* It consists of a series of wires bent 
in the same direction, and the escap- 
ing electricity drives it backward. 
Sometimes points are attached to a 
balanced globe, when the apparatus «2 

Fig. 298. becomes the Electrical Orrery, Tig. 299. Fig. 299. 

This arrangement well illustrates the motion of two bodies around 

a common centre. 

847. -The Mechanical Effects are best shown by means 
of the Ley den Battery of several Jars. 

The Universal Discharger, 

Fig. 300, is needed to show 
these effects readily. It con- 
sists of a central stand of 
glass or ivory, and two rods 
attached to insulating pillars 
Fi ff . 300. " hy universal joints, which 

allow the rods to be placed in any desired position. The 
object to be experimented upon rests upon the stand. 

848. If a small mass of gunpowder be placed upon the 
stand of the Universal Discharger, and a spark passed 
through it, the powder is scattered. The spark passes too 
quickly to produce any other effect. 

But if a moistened string be made a part of the circuit, 
the electricity is retarded, heat is produced, and the powder 
is ignited. 

849. If a block of wood is placed between the points of 
the Universal Discharger, a spark from the Leyden Battery 
splits it into fragments. 

850. So too, a spark may be passed through a card placed 
between the points. In this case, the card is pierced, and 
the hole appears forced outward on both sides. This shows 
that the electricity passes both ways. 

These are some of the mechanical effects of small quan- 
tities of electricity. The same thing may be seen on a 



magnificent scale when lightning strikes. Then trees are 
splintered, and houses torn down, and frequently set on fire. 

851. Heating Effects. One of the heating effects of elec- 
tricity was mentioned in the preceding paragraph. Igniting 
gunpowder, either on the stand of the Universal Dis- 
charger, or in large masses in mines, shows the same effect. 

852. Ether Spoon. The 

heating can be finely shown 
Fig. 301. by holding out an Ether 

Spoon, Fig. 301, to a person on an Insulating Stool. It should con- 
tain just ether enough to cover the knob inside. As he attempts 
to put his finger into it, a spark passes and the ether is inflamed. 

853. The Hydrogen Pistol, Fig. 302, shows that the 
heat often produces chemical changes. The pistol 
contains a mixture of two measures of hydrogen and 
one of oxygen. A chain passes to the inside through 
an insulating tube. "When the knob is brought near a 
prime conductor, a spark passes, and a loud explosion 
follows. The heat of the spark inflames the gases. 

854. Luminous Effects.* Hold the finger out 
Fig. 302. towards a prime conductor: the c/loiv appears on 
the end of the finger, and the brush on the conductor. 

855. If one end of the Jointed Discharger, Fig. 303, be 
connected with the earth, and the other held out to- 
wards the prime conductor, but kept a short distance 
away, the spark passes as a straight line. Increase the 
distance a little, and it takes a zigzag direction. This is 
caused by the differing density of the air. At a still 
greater distance, it splits up into several branches. 

When a jar is discharged in a dark room, the 
difference between its spark, and that of the prime 
Fig. 303. con j llc t or becomes very marked. It appears 
shorter, but thicker and brighter. 

*For good exhibitions of the luminous effects, a dark room is needed. 



856. The Spiral Tube, Fig. 304, shows tlie ordinary- 
spark with good effect. It consists of a glass tube along 
which bits of tin -foil have been pasted. When a spark 
from the prime conductor passes, it appears as a line of 
light, leaping from one piece of tin-foil to the next one 
over the interruption. 

857. The Diamond Jar, Fig. 305, is simply a 
Leyden Jar whose coatings are cut in the form 
of diamonds, and it shows the spark beautifully, 
for when the Jar is receiving its charge a point 
of light appears at each space where the tin- 
foil is removed, and the same effect is repeated 
upon discharging the Jar. 

Fig. 3o4. 

858. The spark from a Jar furnishes the 
means of determining the rate at which electric- 
ity travels. The spark appears to be single, and to Fiff * 305 - 
pass instantanously. But it does not, for if a Jar be dis- 
charged in front of a Revolving Mirror,* the spark appears 
as a line of light. If it passed instantanously, it would 
appear as a spot. 

So too, by passing the spark from a single jar through 
a wire several miles in length, but interrupted in the mid- 
dle so as to allow a spark there and at both ends, the three 
interruptions being placed side by side, 
the three sparks would all be elongated 
by the Revolving Mirror equally. Were 
the passage of the electric- 
ity through the wire instan- 
Fig. 306. taneous, the lines would be 

in the same position, Fig. 306. But the im- 
age as seen in the mirror has the form of 
Fig. 307, the middle one being behind the others. That is, 
the electricity starts from both coatings, and requires a 
measurable time to reach the middle. 

Fig. 307. 

*See Section 473. 



859. The Luminous Pane 

closely resembles the Spiral 
Tube. Fig. 308. It is simply 
a pane of glass with strips of 
tin-foil pasted upon it, and 
cut away at places. Where 
Fig. 308. it is cut away the spark ap- 

pears, since the electricity is interrupted there in its passage. 

860. Magnetic Effects. Finally, if a spark from a Ley- 
den Jar be passed through a sewing needle held vertically, 
the needle becomes a magnet. This accounts for the mag- 
netization of steel tools when a building has been struck 
by lightning. 

Section VI. — The Thunder Storm. 

861. Electricity seems to be present in the air to some 
extent at all times. Free + is more commonly found, but 
— sometimes appears. 

The presence of free electricity can be shown readily by 
means of a long metallic rod terminating in a point at the 
top, and connected with an Electroscope at the bottom. 
Such an instrument so arranged usually diverges. 

The amount of free electricity seems to be greater in 
warm and dry weather than in the winter. It is too, con- 
nected with the little whirlwinds seen so frequently in the 
summer. This is shown by placing an Electroscope in 
such a current, when the leaves always diverge, usually 
with — electricity. 

862. Thunder Storms are local storms which suddenly 
arise on warm summer days, and manifest great accumu- 
lations of electricity. The original development of the 
electricity is not fully understood. Probably the conden- 
sation of the vapor from the air itself is the primary cause. 

863. Condensation results from the meeting of two at- 
mospheric currents, usually at a considerable height above 


the earth's surface. One current is warm, and so contains 
a large amount of dissolved vapor. The chilling of this 
air by the other current reduces the temperature below the 
dew point and causes the precipitation of the vapor, when 
a cloud appears. This is probably accompanied by the 
development of electricity, and the friction of the moving 
cloud probably increases its amount. 

864. Lightning. So soon as a cloud becomes charged, it 
must act inductively upon all neighboring clouds. That 
is, two clouds separated by a layer of air become the 
coatings of an enormous condenser. But as soon as they 
are charged they begin to attract each other, and so they 
gradually move together. After a time, they approach so 
near that the electric tension of the clouds exceeds the 
resistance of the intervening air. The cloucls then dis- 
charge into each other, and the spark is the flash of light- 
ning. Most lightning is produced in this way. 

865. Again: if a charged cloud is separated from the 
earth by a stratum of air, it will act inductively upon that, 
developing electricity of the opposite kind to its own in 
the part immediately under it. Attraction then acts at 
once and the cloud moves towards the earth until a dis- 
charge passes between the earth and the cloud, when the 
lightning strikes. 

866. The Theory of the 

Thunder Storm is well shown 
by the apparatus of Fig. 
309. A Leyden Jar is fitted 
with a copper wire bent as 
shown, and with a pointed 
piece soldered on at D so as 
Fig. 309. to rest upon the knob of the 

Jar. One end of the wire, E, carries a scale pan in which is placed 
a tuft of cotton to represent a cloud. The other end has a short 
piece of glass tubing, C, to serve as an insulating handle, and is 
bent over so as to prevent the escape of the electricity. 


The Jar is charged and placed on a sheet of tin-foil, AB, 
which represents the earth. The copper wire is then 
placed upon the Jar, and the free electricity of the inside 
at once spreads to the cotton, where its presence is shown 
by the divergence of the fibers. But the sheet of tin-foil 
attracts the scale pan and cotton which descend until a 
spark passes and the Jar is discharged. 

If a pointed copper wire be passed through a cork and 
placed on the tin-foil, the discharge no longer passes as a 
spark, provided the Jar be moderately charged, but the cot- 
ton moves away from the point. If the Jar be highly 
charged, the discharge passes from the scale-pan to the 

867. The Lightning Eod acts upon a charged cloud as 
the copper- wire upon the Jar.* It is a metal rod attached 
to the building which is to be protected, and it passes to 
the ground. When a charged cloud approaches it, the 
point silently discharges a portion of the electricity, and 
the cloud moves away. But if a discharge takes place, 
and the lightning strikes, it passes down the rod. 

868. Precautions. The lightning rod must project a 
sufficient distance above the highest point of the building 
to render that the shortest path. It will protect an area 
whose radius is about four times its own height. 

The rod must be continuous, else the lightning is likely 
to leave it at the fracture. 

The rod must have a good ground connection. Theo- 
retically, the area of the portion in contact with the ground 
should equal the roof of the building. Practically, if the 
rod extends to moist earth, and then ends in a sheet of cop- 
per of a few square feet in extent, and is covered with 
charcoal, it is sufficient. 

Lightning rods are usually insulated from the building. 
This seems to be unnecessary, as if the rod meets the above 


conditions, the lightning will follow it without insulation. 
Besides, before th 3 discharge passes, the building itself, 
as well as the rod, becomes completely charged, with elec- 
tricity the opposite to that in the cloud, and it must dis- 
charge itself: it appears to do this as well along the rod as 
through the earth. 

869. Thunder, The passage of the current is accom- 
panied by a loud rumbling sound. This is probably caused 
by the meeting of the masses of air which have been sep- 
arated by the lightning. Its prolonged sound is due to 
the different distances from the ear at which the air meets, 
so that the sound from different points requires different 
lengths of time to reach the ear. 



Section L — The Current. 

870, Discovery. Galvani, when experimenting with 
frog's legs, discovered that if the muscles were touched by 
a plate of metal, and the nerves with a different metal, 
when the two metal pieces touched each other, the legs 
contracted violently. He accounted for the fact by sup- 
posing that the "vital fluid" had passed. 

871. Volta more fully investigated the phenomenon 
and found the cause of the convulsions in the action of 
electricity. He accounted for the electricity by supposing 
it was produced by the contact of the two metal?. But in 



Fig. 310. 

this he erred, the real cause being the 
chemical action of the fluids of the body 
upon one of the metals. 

872. Simple Circuit. The simple voltaic cir- 
cuit is a glass vessel containing dilute sulphuric 
acid.* In this, a plate of copper and another 
of zinc are placed. So long as they remain 
separated, no action takes place. But on con- 
necting them, either directly, or by means of 
a copper wire, as in Fig. 310, bubbles of gas 
arise from the copper plate, and a current of 
electricity passes. If the plates are large, this 
can be detected by placing one wire above the 
tongue and the other below. 

Fig. 311. 

873. Explanation of its Action. Before the plates are 
placed in the liquid, it is probable that the 
molecules of water occupj' all positions, as 
shown in Fig. 311, in which the circles 
represent molecules, of which the light is 
the hydrogen, and the dark the oxygen. After the plates 
of metal are placed in the liquid, polari- 
zation takes place. The zinc which is 
positive attracts the oxygen and repels the 
hydrogen, Fig. 312. As soon as the plates 
are connected, the oxygen of the mole- Fig. 312. 

cules in contact with the zinc plate unites with that to 
form zinc oxide, but leaving the hydrogen 
free, Fig. 313. These hydrogen atoms 
then separate the oxygen from the next 
molecule of water, leaving its hydrogen 
Fig. 313. free. This process continues until the 

copper plate is reached, when the hydrogen having nothing 
to unite with escapes into the air. So the electricity is 
produced on the surface of the zinc plate, and the — runs 

*Dilute sulphuric acid is about ten parts water and one of acid mixed. 
N. P. 17. 


up that plate, while the + moves through the liquid by the 
chemical action upon the molecules, as indicated, and ap- 
pears upon the copper. The copper therefore is called the 
positive pole, or electrode, and the zinc, the negative. 

874. Use of the Sulphuric Acid. When water alone is 
used, the surface of the zinc becomes almost immediately 
coated with a laj^er of insoluble zinc oxide. But the sul- 
phuric acid unites with this zinc oxide to make zinc sulphate 
and water, so presenting a fresh surface of zinc for the 
action of the water, as zinc sulphate is soluble in water. 

875. Quantity and Intensity. The electricity of one 
simple circuit can pass through a second cell precisely 
similar to the first. The action of the second is then added 
to the first, and it doubles the intensity. So any number 
of cells may be connected in this way, and each adds to the 
intensity. But the quantity depends upon the surface 
acted upon. This may be increased by making the cells 
larger, or by connecting the zincs of several cells so as to 
make one large zinc, and the coppers in the same way. 
That is, a battery of separate cells may be connected with 
the copper of one to the zinc of the next and so on, using 
the first zinc as a — pole, and the last copper as a + : giving 
intensity. Or the zincs may all be connected, and all the 
coppers, giving quantity. 

Section" II. — Various Batteries. 

876. Electro-motive Force. The work which a battery 
is capable of doing by transferring the motion of electric- 
ity from one point to another is called its Electro-motive 
Force. In the simple circuit, it is very weak. Besides, it 
constantly grows weaker. This arises from two causes : the 
amount of acid in £he solution grows less, and the zinc salt 
increases. But besides this, and reducing the current still 
more rapidly, is the adhesion of molecules of hydrogen to 



the copper plafce, called Polarization of the Plate. Various 
batteries have been devised to increase the electro-motive 

877. Local Currents. Common zinc contains many im- 
purities, principally metals. These act as — plates, so 
diminishing the electro-motive force, and at the same time 
using the zinc with unnecessary rapidity. But if the zinc 
be amalgamated, that is coated with mercury, the mercury 
dissolves a small amount of the zinc and presents a surface 

of pure zinc to the action of the liquid. 

This removes all local currents, and the 

zinc of every battery should be thus ainal- 


878. Smee's Battery, Fig. 314, consists of two 
plates of zinc and a plate of silver placed be- 
tween them. The silver is coated with finely 
divided platinum, which is black. This has 
very little adhesion for hydrogen and prevents 
polarization of the plate. The three plates are 
usually fastened to a strip of wood, and elec- 
tricity is excited by dilute sulphuric acid. The 

Fig. 314. 

current is weakened by the loss of acid. 

879. Daniell's Battery? Fig. 315, has the merit 
of removing the polarization of the plate, and 
also replacing the sulphuric acid. This renders 
the current constant, and especially adapts the 
battery for use in plating, and as a local tele- 
graph battery. It consists of a copper vessel 
containing a saturated solution of copper sul- 
phate. The vessel acts as the + pole of the 
battery. Crystals of the salt are placed upon 
a shelf to dissolve as fast as the copper sulphate 
is removed, and so keep the solution saturated. 
Inside of the copper, is a vessel of porous earth- 
enware which contains dilute sulphuric acid, 
and the zinc plate is placed in this for the — pole. 

The hydrogen produced by the action of the battery de- 
composes the copper sulphate. This makes sulphuric acid 


Fig. 315. 


which passes into the porous cup, while copper is deposited 
upon the surface of the copper vessel. This action renders 
the current constant. 

880. Gravity Battery. This is a modification of Daniell's, 
in which the liquids are kept separate by a difference in spe- 
cific gravity. The plate of copper is placed in the bottom 
of a glass jar, and an insulated wire passes from it to the 
outside of the jar. Crystals of copper sulphate are placed 
upon it, and the vessel filled about half full of dissolved 
copper sulphate. It is then filled up with very dilute sul- 
phuric acid, and & plate of zinc suspended in that, while an 

insulated wire from the plate becomes 

the — pole. 

881. The Bichromate of Potash 
Battery, Fig. 316, is the most conven- 
ient batte^ for common use. It con- 
sists of a strip of zinc between two 
strips of carbon. The zinc is usually 
attached to a rod, so that it can be raised 
above the liquid when not in use. The 
exciting liquid is a saturated solution 
of bichromate of potash to which about 
one-fifth of its volume of sulphuric 
acid has been added. 

Fig. 316. 

882. Grove's Battery, shown as a single cell in Fig. 317, and as 

Fig. 317. Fi s- dis- 

connected into a battery of six cells to increase the intensity of 



the current in Fig. 318, possesses the highest electro-motive force. 
It consists of a vessel containing the zinc for a — pole, usually 
made as a hollow cylinder, excited by dilute sulphuric acid. In- 
side of the zinc is a porous cup containing strong nitric acid, and 
in this is placed a strip of platinum for the + pole. 

883. Bunsen's Cell, Fig. 319, differs from 
Grove's cell only in replacing the strip of plat- 
inum by a cylinder of gas carbon.* The cell 
is commonly made considerably larger than 
Grove's, and the zinc is made by rolling out a 
thick plate until it is about one -fourth of an 
inch in thickness. A strip of copper is then 
riveted and soldered to the zinc to serve as a 
conductor. This cell requires rather more at- 
tention than Grove's, as salts are liable to form 
in the carbon which prevent the full strength 
of the current. The exciting liquid is dilute 
sulphuric acid, as in the cells previously de- 

Fig. ai'j. 

884. Current produced by 
Heat. If two metals which ex- 
pand at different rates, as anti- 
mony and bismuth, be soldered 
together and heated at the junc- 
tion, Fig. 320, wires passing 
from them to a galvanometerf 
show a current by deflecting 
Fig. 320. the needle. If the junction be 

cooled, the needle is deflected in the opposite direction. All 
metals will act in this way, but antimony and bismuth are 
most effective. A good battery has been devised by Mr. 
Farmer which acts upon this principle. Bars of copper and 
zinc are soldered together alternately and packed in plaster 
of Paris. One side of the plaster is heated ; the other cooled. 

885. The Thermo-Electric Pile, shown complete at P, Fig. 

*The hard carbon formed on the inside of iron gas retorts, 
toee Section 893. 



321, and in section at the 
right, acts by the production 
* of electricity through heat. 
The instrument consists of 
a large number of bars of 
antimony and bismuth sol- 
* dered together in alternate 
order. When a source of 
heat is applied to one end, 
and the other remains cool, a current passes. Used with 
the Astatic Galvanometer, this becomes a very delicate ther- 

Section III. — Effects of the Current. 

Fig. 321. 

886. The effects of the current depend upon its great 
quantity. They may be conveniently divided into Mag- 
netic, Heating, Luminous, and Chemical. 

887, The Magnetic Effects are the deflection of the 
needle, and the making of magnets. 

888. Oersted's Galvanometer, 
Fig. 322, is used to determine the 
laws of deflection. It is a magnetic 
needle suspended in a brass frame. 

889. I. Place the instrument in the 
magnetic meridian, and connect the 
+ pole of a battery with the south 
end, and the — with the north end, 

so that the current shall pass above the needle. The north 

pole of the needle now turns to the west. 

II. Pass the current in the same direction, but by con- 
necting the — ■ with the other binding screw, send the cur- 
rent from south to north under the needle. The north 
pole of the needle moves east. 


III. Pass the current from north to south above the 
needle, and the north pole of the needle again moves east. 

IV. Pass the current from north to south below the 
needle, and the north pole again moves west. 

890. The direction of the deflection can always be deter- 
mined by remembering that if the human body be made 
a part of the circuit, with the current moving from the 
feet towards the head, and then the person face the needle, 
the north pole always moves towards the left. 

891. Galvanometers are instruments for detecting the 
presence and measuring the intensity of electric currents. 
They depend upon the deflection of the needle. 

892. The Sine Galvanometer is a wooden ring around 
which a number of turns of insulated copper wire are 
wound. This is then placed vertically in the plane of the 
magnetic meridian. A large needle is placed in its centre, 
which can turn over a graduated card. When a current 
passes, the needle is deflected, and two currents vary as the 
sines of the angles of deflection. 

893. The Astatic Galvanometer, Fig. 
323, is the most delicate. It consists of an 
Astatic Needle* suspended in a glass case 
by a thread of silk. A large number of 
turns of insulated copper wire is wrapped 
around the lower needle and acts to de- 
flect it, so that a current is multiplied 
many times. This instrument will detect 
the presence of currents whose electro- 
Fiff. 323. motive force is exceedingly weak, 

891. Magnetization. When a current is passed through 
a coil of insulated copper wire, it magnetizes any piece of 
soft iron placed within the coil. Thus when a current is 

*See Section 787, 


Fig. 324. 

passed through the Helix mounted on a 
stand, Fig. 324, the bar of iron shows its 
magnetism by sustaining pieces of iron. 
If the opposite ends of the coil are wrapped 
in the opposite direction, one of the poles 
is in the middle of the iron, and the ends 

become similar poles. 

895. The Helix and Semicircular Rings, Fig. 325, 
act in the same way. When a current passes 
through the small coil of copper wire, the soft iron 
rings are magnetized, and can be separated with 
difficulty. When not magnetized, they fall apart 
by their own weight. 

896. The Electro-Magnet, Fig. 326, is made of a Fig. 325. 

piece of soft iron in the shape of a 
letter U, with a coil of insulated 
copper wire wound around the 
ends. The wire must be wound in 
the same direction, else one of the 
poles will be in the middle. When 
the coil is wound from left to right, 
the north pole will be the end 
where the current enters, while the 
other end is the south pole. 

The iron is instantly mag- 
netized when the current is 
made, and it will sustain a great 
weight. But when the current 
is interrupted, it at once loses 
Fig. 326. its magnetism. 

Electro-magnets have been applied to numerous uses, 
such as separating iron from brass, lifting weights, and 
lately in separating bits of iron from wheat before it enters 
the mills for grinding. But by far the most important ap- 
plication is the Telegraph. 

897. Morse's Telegraph, Fig. 327, consists of an electro-magnet 
whose armature of soft iron moves a lever. This lever is so set 


by screws that its motion 
is stopped before the ar- 
mature reaches the mag- 
net, else the residual mag- 
netism of the iron would 
prevent rapid working. 
The lever carries a style, 
which moves and marks 
Fig. 327. a strip of paper, which is 

drawn by clock work. The message is recorded in a series of dots 

and dashes. 

898. The Circuit The conducting wire from one pole 
of the battery runs to the ground and ends in a large cop- 
per plate. The other conducting wire of the battery runs 
to the operating key and there enters the post or anvil by 
the wire. When the key is brought down by pressing the 
knob, the circuit is closed: when the pressure is removed, 
the key rises and interrupts the circuit. The current leaves 
the key from the middle by the wire and goes through that 
to the receiving instrument, which may be many miles 
distant. It reaches the receiving instrument by the line 
wire, passes through the electro-magnet, and then escapes 
through the other wire to the ground, where the wire ter- 
minates in a copper plate. It returns through the ground 
to the battery. 

899. The Relay. If the circuit is more than thirty miles, the in- 
tensity of the current becomes too weak to work the receiving 
instrument. This arises because of the resistance of the conduct- 
ing wire, and because no way of perfect insulation has yet been 
devised. Hence some of the electricity escapes to the ground at 
each post. To obviate this difficulty, the Relay, Fig. 328, is used. 
It consists of an electro-magnet, E, whose armature, A, is hung so as 
to move very easily. This magnet is connected with the line wire, 
while the receiving instrument is only connected with a small 
battery in the room where the message is received, called a local 
battery. The current from this enters the post, C, and passes 
thence through the post and screw N, and down the rod p, which 
is the lever of the armature A, and rod o, to the binding screw Z, 


and thence to the receiving instrument, through that, and back 

Fig. 328. 

to the battery. So this current is broken except during the time 
when a current is passing through the magnet E. All the work 
required of the main current is to move the lever p through a very 
small distance, so closing the circuit of the local battery, and a 
spring, r, returns it to its original position. 

Most operators at present read entirely by sound. This 
does away with all occasion for local batteries and receiving 

900. A helix of wire through which a current is passing 

is itself a magnet. It will 
hold up pieces of iron, mag- 
netize steel, or if suspended 
so as to turn freely, will 
point north and south. So 
two helices will attract and 
repel each other, like mag- 
nets, as is shown by Fig. 329. 

The Earth's Magnetism. This last phenomenon, in con- 
nection with the production of currents by heat, affords an 
explanation of the earth's magnetic properties. It is prob- 
able that the sun, as it apparently moves west in its daily 
course, heats the part of the earth directly under itself. 

Fig 329. 


This produces a current of electricity to the west, which 
being beneath the needle deflects the north pole to the left, 
or North. 

Heating Effects. 

901. The heat produced by the battery is due to the re- 
sistance which the current meets on its passage. This is 
in two places, the battery, and the wire where the work is 
done. The former is essential, for it cannot be removed. 
But all that is required to overcome the resistance in that 
part of the circuit is so much taken from the power to do 
work at another point. Hence by increasing the surface 
of the plates, that is the quantity, the heating effects can 
be increased. 

The heat of the current can be well shown by passing 
the current through a fine iron wire. The wire will be 
heated red hot, or melted. This is due to its own resistance 
to the passage of the current. 

The force of the battery appears only as heat when it 
no longer moves as electricity. Hence the heat is in in- 
verse ratio to the conductivity of the wire. So only such 
inetajs as offer considerable resistance can be much heated 
by the current. 

902. Firing Powder. The heat of the current has been 
successfully applied to igniting powder. The powder cup, 
a shallow vessel containing two copper conducting wires 
whose ends are connected by a short piece of fine platinum 
wire, is used to show this. The platinum wire is covered 
with powder, which is ignited as soon as the current passes. 

In this way, mines are fired. A fuse is used Avhich has a 
short piece of platinum wire imbedded in powder, connect- 
ing conducting wires. When the current passes, the heat 
in the platinum wire fires the powder. 

903. The same method has been applied to lighting the 




gas in large buildings. Conducting wires pass to the sev- 
eral burners, and there they are connected by platinum 
wires which cross the openings of the burners. The es- 
caping gas is lighted by the heated wire. 

The Electkic Light. 

904. When the resistance offered by a conductor to the 
passage of the current is sufficient, the temperature is raised 
to the point of incandescence, and the conductor becomes 
a source of light. 

905. If the conductor consists of two parts slightly 
separated, the force of the current is sufficient to move 
minute particles across the vacant space. But the resis- 
tance is then sufficient to make all the moving particles 
incandescent. A discharge of this kind is called disruptive, 
and the heat produced is very intense. All forms of the 
electric light are produced in one of these ways. 

906. The disruptive discharge can be readily shown by 
connecting two or three common Bunsen cells for intensity. 
Then connect an insulated conducting wire to the — pole 

of the last cell, and bring 
it down upon the carbon 
of the first cell. The light 
will at once appear, while 
the wire will be rapidly 

907. The Arc. To pro- 
duce the Voltaic Arc, two 
pieces of boxwood char- 
coal are used. These are 
placed in a frame, as 
shown in Fig. 330, and 
the upper one is connect- 
ed with the + pole of a 

Fig. 330. 



battery of forty or fifty cells connected for intensity, and 
the lower one with the — pole. After bringing them into 
contact, and then separating them for a short distance, par- 
ticles of incandescent carbon pass between them. This 
produces a very intense white light. 

When the arc is made in the open air, the points are 
slowly consumed. This is entirely overcome by placing the 
points in a vacuum. 

The + point diminishes the more rapidly. This is caused 
by the transference of particles from that carbon to the 
— . So the carbons must be constantly moved towards 
each other, the + moving the greater distance. 

908. The electric light made in this way is the most in- 
tense artificial light known. Hence it is often used, in 
connection with a clock-work regulator, for light-houses. 
A great improvement has been made in the light for this 
purpose by making the + pole a disk of carbon, and mov- 
ing the — around its edge. 

This electric light is not suited for general illumination, 
since the area of the luminous matter is very small. So the 
light, though very intense, lacks quantity. 

909. The Jabloukoff Candle, Fig. 331, 

contains two small carbon pencils placed side 
by side, about a fourth of an inch apart, the 
space between being filled with clay. To 
produce the current, a small piece of plati- 
num wire is placed between the carbons, 
which is at once vaporized. As the points wear 
away, the clay melts and vaporizes, so that 
(he ends remain at the same distance from 
each other. Practically, this light is operated 
by the current from a Magneto Machine, which reverses 
the direction of the current, and burns both carbons equally. 

Fig. 331. 



910. The Edison Light depends upon 
incandescence. Fig. 332. A piece of card- 
board is cut out in the shape of a horse- 
shoe and baked until it becomes pure car- 
bon. It is then placed in a glass globe, 
attached to platinum conducting wires 
melted into the glass, and the globe ex- 
hausted as completely as possible and 
sealed. The current renders the carbon 
incandescent, and so long as the globe is 
free from air, there is no loss of carbon. 
The Edison light is much less intense 
than either of the other forms, and its 
area is also much greater. Hence it is 
better for common use. Its greatest fault 
is the different rates of expansion of the platinum con- 
ducting wires and the glass, which must ultimately allow 
air to enter the globe. 

Chemical Effects. 

911. When a current of two or three Bunsen cells is 
passed through water which contains sul- 
phuric acid, hydrogen appears at the — pole, 
and oxygen at the + , Fig. 333. Collecting the 
gases, the volume of the hydrogen is double 
that of the oxygen. This shows that the 
current has separated the water into its ele- 

912. Since water has never been decom- 
posed when free from acid, though very pow- 
erful batteries have been employed, it seems probable that 
the current really acts upon the molecule of sulphuric acid. 
The — pole removes the hydrogen atoms from it, and the 
+ pole one of the oxygen atoms, leaving sulphuric an- 
hydride. This, however, at once unites with another mol- 



ecule of water, and becomes sulphuric acid again. So the 
decomposition of the water is accomplished indirectly, but 
not directly. 

913. Soo too, most salts can be decomposed by the cur- 
rent. In case the salt contains two elements, one goes to 
the + pole, and the other to the — . When the salt con- 
tains several elements, one element goes to one pole, and a 
group forming a molecule to the other. 

914. Electro-plating is one of the most important applications 
of the chemical work of the current. To obtain a deposit of copper 
upon any object, it is first carefully cleaned. It is then suspended 
in a saturated solution of copper sulphate, and connected with the 
— pole of a battery of a single cell, B, Fig. 334. A plate of copper 

Fiff. 334. 

of about the same area as the object to be plated is connected with 
the + pole. The current acts upon the first molecule of the cop- 
per sulphate, moving the sulphuric acid to the copper plate and 
causing chemical union. This makes copper sulphate. The copper 
set free from the first molecule unites with the sulphuric acid of 
the second molecule, and so on until the object is reached, where 
the copper is left adhering to its surface. 

915. Electrotyping. Medals may be copied, or a page of 
type prepared by this process. A cast of the medal or 
type is made of plaster of Paris or wax. This is a reverse 
of the type desired. This cast is then covered with graph- 


ite to render it a good conductor, and suspended in the bath 
as before. 

Any substance desired can be deposited in this way. Sil- 
ver is best deposited from the cyanide, and nickel from the 
chloride. Some one salt of each metal gives better results 
than any other. 



Section I. — Production of Induced Currents. 

916. When a current of electricity from a battery passes 
through a coil of wire, it induces a temporary current in 
any neighboring wire. So also when the current is broken, 
a similar temporary current is produced. 

917. Induction Shown. 

A central bobbin, Fig. 335, 
has a coarse insulated cop- 
per wire wound upon it. 
This is called the Prima- 
ry Coil. Outside of this, 
a second coil of fine in- 
sulated wire, several times 
the length of the first, 
is wound, called the Sec- 
ondary. The ends of this 
Fig. 335. Secondary are connected 

with a Galvanometer, by means of the binding screws, 

shown at the side. 

I. Connect the ends of the Primary with the poles of a 

battery, and the needle of the Galvanometer is deflected. 


This deflection is in the direction to show a current in the 
opposite direction to that in the Primary. This induced 
current does not continue, for the needle soon returns to 

II. Break the connection with the battery, and the Gal- 
vanometer needle is deflected, but in the opposite direction 
to the previous deflection. This shows thai the second 
current passes in the same direction as the primary current. 

918. Induction by Change of Distance. Induced cur- 
rents may also be produced without interrupting the pri- 
mary current simply by changing the distance between the 
coils. This may be readily shown by having the coils wound 
separately, Fig. 335, so that the Primary can pass inside of 
the Secondary. When the Primary is pushed into the 
Secondary, the needle is deflected in one direction; when it 
is removed, the deflection is in the opposite direction. 

919. Induction by Magnets. If a coil of wire be wound 
around a small bar of soft iron and then connected with a 
Galvanometer, the needle is deflected when the poles of a 
horseshoe magnet are brought near the iron bar. The 
needle is also deflected, but in the opposite direction, when 
the magnet is removed. 

In the same way, if a bar magnet be thrust into a hollow 
coil, the needle is deflected, and is deflected in the opposite 
direction upon its removal. This is readily shown by the 
apparatus of Fig. 335, by removing the outer coil, and using 
a bar magnet with that, while the conducting wires are still 
connected with the Galvanometer. The deflection is in 
one direction, if the north pole be forward: but in the op- 
posite direction, if the south pole be forward. 

These simple experiments show how induced currents 
are produced. Their effects show that they are similar to 
the currents produced by the battery. They are, however, 

N. P. 18. 



much more intense, and in this respect resemble Frictional 

920. Two methods of producing induced currents are of 
special interest, the Induction Coil, which is excited by a 
battery; and the Magneto Machine, in which the induced 
current is excited by the magnet, and this is becoming the 
method of the greatest practical importance, since it is 
used to produce the Electric Light. 

921. The Induction Coil, 

Fig. 336, consists of a coil 
of coarse copper wire, the 
separate layers of which 
are carefully insulated, to 
act as a Primary. Inside 
of this, is a bundle of soft 
iron wires, which by their 
inductive action, greatly 
increase the strength of 
the current. The second- 
ary coil, C, often contains 
several miles of wire, and 
ends in two poles sup- 
ported upon glass pillars. 

Fi *- 336 - 922. To make and 

break the current with the greatest ease, the primary cur- 
rent passes through an anvil which is struck by a hammer 
moved by the ratchet wheel b. Every time a cog is reached, 
the current is interrupted, and the number of the sparks 
is determined by the rotation of the ratchet. 

923. When a current is interrupted, a wave of electricity 
in the contrary direction to the original current enters the 
wire. This largely detracts from the effect of the induced 
current. In the Induction Coil, the injurious effect is 
avoided by allowing this extra current to enter a Condenser 
made of tin-foil between layers of silk. When the primary 


current is again made, the Condenser is discharged through 
the priniar} r . 

924. The Magneto Machine consists of a Magnetic Battery,* or 

a pair of batteries placed in opposite directions, N and S, Fig. 337, 
and an armature. The armature is made of a bundle of soft iron 

Fig. 337. 

wire, with a large amount of fine insulated copper wire wound 
around it to make a coil. The armature can be revolved by a pulley, 
and the magnets produce a current of electricity in the wire. The 
direction of the current is changed by passing through a brass 
cylinder cut along each side, and a spring. The spring can touch 
only one portion of the cylinder at a time and hence must change 
the current twice at each revolution. The arrangement is called 
a Commutator. 

925. When made of small size and turned by hand, this 
instrument is frequently used for producing weak currents. 
It is of special interest because enormous machines driven 
by steam, containing an immense number of magnets all 
acting upon the same armatures, have been constructed 
lately. Some of these are now used by telegraph companies 
in place of batteries. 

926. The Telephone. The current of the telephone is 
induced by a magnet and armature. The sound condensa- 
tion moves the armature of the instrument nearer the 

♦See Section 768. 


magnet. This induces a current of electricity in one di- 
rection around the wire, as the magnetism of the magnet 
is strengthened. This current traverses the entire circuit, 
so strengthening all the connected telephone magnets in 
the same way. Hence every armature will move towards 
the magnet precisely as the first. But when the rarefaction 
of the sound wave reaches the armature, it is drawn fur- 
ther from the magnet. This induces a current in the 
opposite direction and weakens all the magnets. The 
elasticity of all the other armatures moves them away. 
So the sound pulses produce electric currents which traverse 
the wire and are again transformed into sound at each 
telephone. * 

Section" II. — Effects of Induced Currents. 

927. The effects of the induced current differ but little 
from those of othe^r forms of electricity. With a good 
Induction Coil, all the xperiments of Frictional Electric- 
ity can be performed, and the only difference noticed is 
that the intensity is rather less. But the quantity is much 
greater, and the instrument is independent of the state of 
the atmosphere. 

The special effects of these currents are Physiological 
Heating \ and Luminous. 

928. Physiological Effects. These can be shown by a 
powerful battery, or even by a Leyden Jar, as they all affect 
living bodies similarly, but the induced current shows them 
most readily. But a small coil must be employed, as the 
current from a large coil is dangerous. 

Electricity acts primarily upon the nerves. Hence all 
the nerves in the path of the current are stimulated to 
activity. Thus if a current be passed through the body 
from hand to hand, the muscles contract. If the current 

*For description, see Section 477. 


passes through the tongue, a peculiar taste is experienced. 
A current through the eye produces the sensation of a flash 
of light. 

A powerful current violently contracts the muscles. 
Often this makes the entire system rigid, and if it is long 
continued, it is exceedingly painful. 

The electric current passes much more rapidly than the 
nervous force. Hence an interrupted current ceases before 
it is felt, and it is probable that death from lightning is 

929. The use of weak induced cur- 
rents is quite common in medicine. 
For this purpose, the coil of Fig 338 
is used, in which the primary current 
traverses a small electro -magnet. This 
Fig. 338. draws down an armature, so inter- 

rupting the current. A spring at once carries the armature back, 
and again makes the current. This is repeated with great rapidity. 

These secondary currents are employed in cases of de- 
ficient nervous action, as paralysis, to stimulate the nerves. 
They are also used to stimulate glands whose action is de- 

The muscles do not cease to respond to the stimulus of 
currents immediately at death. Hence they are often used 
to resuscitate persons who have been asphyxiated, either by 
irrespirable gases, or by drowning. 

930. Heating Effects. The heating effects of induced 
currents can be easily shown by attaching a small piece of 
wire, platinum, for example, to each pole of the Induction 
Coil. After a few sparks have passed, the — becomes in- 
tensely heated, and perhaps fuses. The + remains cool. 

A beautiful experiment is to moisten the surface of a 
large cork with sulphuric acid and thrust into it a cop- 
per wire connected with the — pole of the coil. Now 
bring the + pole near the — , but dipping into the sul- 
phuric acid. The heat at once evaporates the water from 



the acid, the acid then makes the cork a conductor, and a 
large surface of the cork appears illuminated. 

931. Luminous Effects. The last experiment shows one 
luminous effect, connected with heat. 

Aurora Tube. The following experiment uses 
the Guinea and Feather Tube, Fig. 339, and is one 
of the most instructive. The tube is screwed to 
the plate of the Air Pump, and the — pole of the 
Induction Coil attached to the plate, and the + to 
the top of the tube. Before exhaustion, no elec- 
tricity passes. As the exhaustion proceeds, a point 
is reached where light appears at the top of the 
tube. Soon after, flashes pass the whole length, 
the color depending upon the degree of exhaus- 
tion. If the finger is placed at one side of tube 
induction takes place, and the light seems to touch 
that point. 

932. The above experiment indicates, that 
the Aurora seen in northern regions is simply 
the passage of electricity through the upper 
regions of the air. The cause of the electric- 
Fig. 339. ity does not seem to be determined. Certain 
observations seem to indicate that it may be due to changes 
taking place in the Sun's atmosphere, perhaps 
to explosion of gases like hydrogen. 

933. Abbe Nollet's Globe, Fig. 340, is a globe partly 
filled with water. The globe is fitted into the top of 
a receiver air tight, and placed upon the plate of an 
Air Pump. The top is connected with the + pole and 
the plate with the — , and the receiver is exhausted. 
The current then fills the whole with light. 

If quinine dissolved in water and rendered 
clear by a little sulphuric acid is substituted for 
the water, the Globe shows fluorescence. 

Fig. 340 

934. Oeissler Tubes are tubes that have been exhausted 


so that only a trace of gas remains. They are then placed 
in the path of the induced current. They glow with light 
whose color depends upon the kind of gas which they con- 
tain, and also to some extent upon the degree of their ex- 
haustion. They can be made in any desired shape, and 
their effect is very beautiful. Fig. 341 shows some of the 


Fig. 341. 

many forms.* The bulbs are often made of uranium glass, 
when they shine for a short time after the current ceases, 
as the glass becomes fluorescent with a pale green light. 
No. 2 is such a tube. Or the current may pass through a 
central tube which is surrounded with a liquid, as quinine 
dissolved in dilute sulphuric acid, which becomes fluores- 
cent by induction from the current. 

Many other beautiful experiments can be performed to 
show the light of induced currents. All, however, act 
upon the same principle as these. 

935. Radiant Matter Tubes. Though the exhaustion is 
carried to a high degree in the ordinary Geissler tubes, it 
is by no means complete. Sufficient gas remains to carry 
the electricity without being itself changed in any per- 

*These forms are kept by Messrs. E S. Ritchie & Sons, Boston, Mass. 


ceptible way. But Prof. Crookes has demonstrated that 
when the exhaustion has been carried one step further, the 
remaining matter, when acted upon by the electric current, 
shows some peculiar properties which he explains as due 
to a change of state analogous to the change from a liquid 
to a gas. Whether his explanation be correct or not, the 
phenomena are beautiful illustrations of the effect of elec- 
trical action. 

To show these phenomena, tubes are exhausted so that 
the pressure of the gas remaining does not exceed one mil- 
lionth of an atmosphere. An electric current from an 
Induction Coil reaches poles placed inside the tube, and 
these, of platinum as usual, are made into thin plates so as 
to present a large surface in action. Now the molecules 
of the remaining gas seem to move away from the — 
pole towards the + in straight lines, and they continue 
their course until stopped by the walls of the tube, or by 
some intervening obstruction. 

936. Matter moving in this way so affects the walls of the 
glass tube as to make them fluorescent, so that they shine 

with a pale mellow light* 
But if a plate of platinum 
be placed within, as in 
Fig. 342, that intercepts 
the molecules and so seem s 
to cast a shadow. It is 
not really a shadow, how- 
ever, only a place where 
Fig. S 42. the tube is not struck by 

the moving molecules. The manner of movement of these 
molecules does not differ from that of the molecules of 
gases, but as they do not strike other molecules frequently, 
they move further in a single direction. That is, the wiean 
free path is increased. But when they have once reacln d 



a solid, either their motion is stopped altogether, or they 
are deprived of the power to emit light. 

Other substances besides glass can be rendered fluorescent 

in a similar way. 
Thus if a mass of 
rubies be placed in 
front of such a — 
pole, see Fig. 343, 
they begin to shine 
with a peculiar soft 
radiance. The light 
moves away from 
Fig - 343 - them in straight 

lines, as from any other source. 

There is, however, a limit to the action of these moving 
molecules, for if the current is allowed to act continuously, 
after a time, the fluorescence ceases. Some substances 
regain the property of fluorescence after a period of rest; 
others do not, but after once being acted upon, ever after 
remain unaffected. This indicates a rearrangement of the 



1 Talc. 

2 Rock Salt. 

3 Calcspar. 

4 Fluorspar. 

5 Apatite. 

6 Feldspar. 

7 Quartz. 

8 Topaz. 

9 Corundum. 
10 Diamond. 


This table gives the breaking load, in pounds, that a square inch of 
section will hold. The English system of weights and measures 
is used, because most mechanics still^mploy that system. 



Fir, Pine. 



This table gives the weight in kilogrammes that a bar one millime- 
tre square can support without breaking. 

Sudden Stress 

Gradual Stress. 

Cast Steel 




65 7 


61 1 


40 3 

Platinum _ _ 

Silver _ 












c. 5 





c 2 








5 > 








cc o 





o > 

S a 

1. 369 

















1. 078 






24. 013 


1. 085 







1. 094 
1. 101! 




















1. 109 










1. 126 














1. 070, 














1. 152 





70 1. 854 





• I Specific 
o Gravity. 
o 1 







• 1 Specific 
cd Gravity. 









CO C3 















^p 1 Specific 
co Gravity. 
O 1 






'o > 























.942 1 


































Anthracite Coal 


Platinum 21.53 



Beech Wood... 




Olive Oil.. 


Common Salt.. 




Sulphuric Ack. 




Steel _. 



Cork . 




Air _. . 

1 000 






Iceland Spar 


Yellow Pine... 


Carbonic Anhydride... 


Iron, Wrought. 






Iron, Cast 





Ivory _.. 




Marsh Gas 


Lead.. _ 













Hydroch. Acid. 


Sulphurous Anhydride - . 

2. 247 

Oak Wood 










Solids at 
Ordinary Temperature. 



Solids at 
Ordinary Temperature. 





White Wax. 




Wood's Fusible Metal 








LiquidR at 
Ordinary Temperature. 

Gold - 









Bisulphide Carbon 


Lead . 







Chloroform _ . 






Rose's Fusible Metal 


Mercury _ 




Hydrated Ammonia . 


Sodium .. 


Hydrochloric Acid. . 




Nitric Acid. 




Oil Turpentine . 


Sulphur .. 



Sulphuric Acid. 


Tin .. .... 







The conduction of heat is given to accord with the results obtained 
by Messrs. Wiedemann and Franz: in electricity, the results of 
Matthiessen are given. 

Name of the Metal. 

for Heat. 
Silver = LOO. 


for Electricity. 

Silver =100. 













Copper ._ 


Iron _ 


Lead -_. 

Platinum. _ 









Name of the Color. 

Blue ... 
Indigo . 


of Waves Made 

Each Second. 


of one Undulation 

in Millimetres. 

" 609 
" 576 
" 536 
" 497 
" 470 
" 442 



Abbe Nollet's Globe 278 

Aberration, Chromatic 205 

Spherical.... 205 

Absorption hygrometer 157 

Achromatic lens 20G 

Acoustics 99 

Acoustic figures 126 

Action and reaction 35 

Adhesion 14 

to gases 1G 

of liquids 16 

to liquids 16 

between solids 14 

Agonic line 229 

Air, buoyancy of 88 

downward pressure of . . 86 

moisture of ; . . 155 

pump 84 

upward pressure of 86 

Alloys 144 

Apparatus, Savart's 115 

Arch 57 

Archimedes' principle' 61 

Armature 237 

Artesian well 76 

Atmosphere 83 

" constituents of 81 

Atom 1 

Attraction 11 

by magnets 225 

capillary 17 

molecular 12 

Attwood's machine 29 

Aurora 278 

Axes of lenses 201 

of mirrors 189 

Balance 26 

wheels, compensating . . 142 

Balloons 89 

Barker's mill 79 

Barometers 90 

Aneroid 92 

cistern 91 

Fortin's 92 

variations of 92 

Battery, bichromate of pot- 
ash 260 

Bunsen's 261 

Daniell's 259 

gravity 260 

Grove's 260 

Leyden 244 

Smee's 259 

Baume's hydrometer 64 

Beam, deflection of 65 

fastened 56 

form of 57 

of light :179 

supported at end 53 

Beats Ill 

BeUows 116 

hydrostatic 69 

Body defined 1 

falling 25 

falling, laws of 28 

luminous 179 



Body, non-luminous 179 

Boiler explosions 159 

steam 175 

Boiling point. 149 

Bottle, specific gravity 64 

Boyle's law 93 

Brace 58 

Bramah's press 67 

Breast wheel 78 

Brittleness 10 

Bunsen's photometer 187 

Buo3 T ancy of air 88 

Burning glass 116 

Calibration 139 

Camera 210 

Candle flame 180 

power 186 

Capillarity 17 

Capillary attraction .' 17 

repulsion 18 

Capstan 48 

Cartesian diver 62 

Caustic curves 265 

Centre of gravity. 23 

Centrifugal force 50 

Centripetal force 50 

Chladni's law. . . 127 

Chords 118 

Clocks 32 

Clothing, color of 167 

Clouds 157 

Coefficient of expansion. . . .137 
Cohesion of liquids. 14 

of solids 12 

Cold and hot 135 

Cold by expansion 152 

Color 11 

of bodies 2C0 

Colors, complementary 200 

mixed 200 

Conrpass, mariner's 230 

surveyor's 230 

Combustion 169 

Compressibility 8 

Concave mirrors 191 

images by 192 

Condenser 83 

electrical 242 

Liebig's 155 

Conduction 160 

Conductometer 160 

Conductors of electricity. . . 235 

of heat 160 

Convection 162 

Convex mirrors 193 

Cord 44 

Coulomb's torsion balance . . 13 

electric 237 

Couple 40 

Crane 48 

Critical angle 197 

Crushing strain 55 

Cryophorus 153 

Crystallization 145 

Cubic expansion 137 

Currents, local 259 

Daniell's hygrometer 156 

Davy melting ice 174 

Declination, variation of . . . . 229 

Derrick 48 

Dew 158 

Diamond Jar 252 

Diapason 104, 117 

Direction, line of 25 

Dissolving views 211 

Distillation 154 

fractional 155 

Divergent rays 179 

Diving bell 98 

Divisibility 7 

Doppler's principle 106 

Double touch 213 

Drummond light 181 

Ductility 10 

Earth, flattening of ......... . 51 

Ebullition .149 



Eccentric 175 

Echo Ill 

multiplied 112 

Edison's light r ... 270 

Effects of points 239 

Elasticity 8 

of flexure 14 

of torsion 13 

of traction 12 

Element 2 

Electric arc 268 

light _ • 2G8 

Electrical chain 249 

chime 249 

induction 240 

insulation 236 

orrery 250 

machine, Holtz's 247 

machine, plate 246 

whirl 249 

wind 249 

Electricity 224 

detection of 236 

distribution 239 

effects of ..248 

Frictional 234 

Induced 272 

kinds of 224 

laws of 237 

magnetization by 233 

polarity of 235 

position of 238 

production of 245 

quantity and intensity . . 258 

rate of moving 252 

Electro-magnet 265 

Electrometer 237 

Electro-motive force 258 

Electro-plating 271 

Electroscope, gold leaf 236 

Electrotyping 271 

Electrophorus 245 

N. P. 19. 

Equilibrium 25 

of connected vessels .... 71 

of different liquids 72 

indifferent 26 

stable 26 

unstable 26 

Ether 179 

spoon 251 

Evaporation 148 

Exchanges, theory of 165 

Expansion 136 

coefficient of 137 

cubic 137 

linear 136 

of gases 81, 137 

of liquids ...137 

of solids 136 

superficial 137 

Experiments, Pascal's 90 

TorriceUi's 90 

Explosions, boiler 159 

Extension 5 

Eye 215 

Fahrenheit's hydrometer ... 64 

thermometer 140 

Far-sightedness 217 

Figures, Acoustic 126 

Lissajous' 128 

Films, colors in 218 

Fire engine 98 

syringe 170 

Firing powder 267 

Flexure, elasticity of 14 

Fluxes 144 

Foci, concave lenses 204 

conjugate 202 

convex lenses 201 

Focus of mirrors 191 

Fog 157 

Force, constant 34 

defined 2 

external 34 

impulsive 34 



Force, moving 35 

unit of 35 

Forces, centripetal 50 

centrifugal 50 

composition 36 

parallel 39 

parallelogram of 37 

parallelopiped of 38 

resultant of 36 

resolution of 36 

undulatory 40 

Forcing pump 98 

Fountain 72 

Hero's 96 

Frames 57 

Franklin's heat experiment . 167 

Freezing mixtures 147 

Fresnel's experiment .-. . 217 

Friction 14 

rolling . 15 

sliding 15 

Frost 158 

Fulminating pane 243 

Fundamental note 118 

Fusion 143 

change by Pressure 143 

laws 143 

vitreous 143 

Gallery, whispering 112 

Galvani's experiments 256 

Galvanometer, astatic 263 

Oersted's 2G2 

sine 263 

Gas, denned 3 

Gases, expansibility of 81 

expansion of... 137 

kinetic theory 82 

mechanics of 81 

osmose of * 21 

specific gravity 65 

Geissler's tubes 278 

Glass, burning. . , 116 

$ ramme 5 

Gravitation 22 

Gravity, centre of 32 

Gridiron pendulum . 141 

Hail 157 

Hardness 10 

Heat, absorption 163 

at different seasons 165 

chemical action 168 

conductors of 160 

dark 164 

defined 138 

effects of 136 

luminous 164 

motion of 160 

radiant, laws of 164 

reflection of 167 

sources of 168 

transmission of 168 

unit of 171 

Helix 264 

Hemispheres, Magdeburg ... 87 

Hero's fountain 98 

Hopkins' tube Ill 

Horizontal 23 

Hot and Cold 135 

Hydraulics 74 

Hydraulic ram 77 

Hydrometer, Baume's 64 

Fahrenheit's 64 

Hydrogen pistol 251 

Hydrostatic bellows 69 

paradox :' 69 

Hydrostatics 66 

Hygrometers 159 

Hygrometric state 155 

Hypothesis 4 

Iceland spar 221 

Ice machines 153 

Images by apertures 185 

by concave lenses 204 

by concave mirrors 192 

by convex lenses 202 

by convex mirrors 194 



Images by plane mirrors 189 

Impact of elastic bodies 35 

of inelastic bodies 35 

Impenetrability 5 

Indestructibility 4 

Inclined plane 51 

Induction coil V 921 

of the earth 233 

Inertia 6 

Instruments, mouth 124 

musical 120 

optical 206 

wind 123 

Insulating stool 249 

Interference of light 217 

of sound 110 

Intervals 118 

Jabloukcff s candle 2G9 

Jets 74 

downward 75 

side 75 

upward 67 

Jointed discharger 251 

Joule's apparatus 174 

Kaleidoscope 190 

Kinetic theory of gases . 82 

Koenig's manometric flames . 130 

Law, Physical 3 

Boyle's 93 

capillarity 18 

Chladni's 127 

of ebullition . . 150 

of electricity 237 

of falling bodies 28 

of fusion 143 

of gravitation 22 

of pendulum 31 

of intensity of light 185 

of radiant heat 164 

of refraction 194 

of reflection 109 

of sound 102 

of strings 120 


Lenses 201 

images by 202 

Leslie's experiment 152 

Levelling 73 

Level, spirit 73 

water 73 

Lever 44 

classes of 44 

Leyden Jar 243 

Liebig's Condenser 155 

Light, interception of 188 

intensity of 183 

movement of 182 

recomposition of 199 

reflection of 188 

sources of 179 

undulatory theoiy 217 

Lightning 254 

rod 255 

Line of direction 25 

Liquid defined 3 

Liquids 59 

compressibility of 60 

elasticity of 60 

expansion of 137 

general properties 59 

specific gravity 63 

Lissajous' figures 128 

Loops 121 

Luminous bodies 179 

pane 253 

Lyman's apparatus 42 

Machines moving in water . . 80 

magneto electric 275 

simple . . . '. 44 

Magdeburg hemispheres 87 

Magic Lantern 211 

Magnetic battery 227 

curves 225 

equator 231 

induction 226 

poles 231 

needle ' 229 



Magnetic needle, variations 

of 229 

Magnetism 224 

of earth ....266 

Magnets, artificial 225 

broken 226 

natural 224 

poles of 225 

Magnetization, methods of . .232 

Malleability 10 

Manometers 94 

compressed air 94 

open air 94 

Marcet's globe 151 

Mariotte's tube 93 

Materials, strength of 54 

Matter 1 

properties of 4 

states of 2 

Mechanics 43 

of gases . 81 

of liquids 59 

of solids 43 

Membranes, vibrating 128 

Mercurial pendulum 142 

Metre 5 

Microscopes 208 

Mirage 197 

Mirrors 189 

axes of 189 

concave 191 

concave, images by 192 

convex 193 

convex, images by . . 194 

plane, images by 189 

Mixed colors * .200 

Mobility 9 

Molecule 1 

Morse's telegraph 265 

Motion, absolute 9 

relative 9 

Mouth instruments 124 

Musical scale 118 

Musical sounds 114 

, sounds, intensity 114 

Music, theory. 119 

Near sightedness 216 

Needle, astatic 232 

dipping 231 

Newton's disc 200 

first Law 6 

Kings 219 

Nichol's prism 221 

Nodes 121 

Normal tuning-fork 118 

Note, fundamental 118 

Odor 11 

Opera glass 208 

Optical axis 221 

Optics 179 

Optical instruments 206 

Organ pipes 125 

Oscillation, centre of 31 

Osmose 20 

of gases 39 

Overshot wheel 78 

Paddle wheel 80 

Papin's digester 152 

Parachute 89 

Parallel forces 39 

Parallelogram of forces 37 

Parallelopiped of forces 38 

Pascal's experiments 90 

law 66 

Pencil of light 179 

Pendulum 31 

compensating 141 

compound 31 

electric 242 

laws 31 

simple 31 

Penumbra 184 

Phenomenon 3 

Phonograph 133 

Phosphorescence 181 

Phosphorous, light of 181 



Photometer, Bunsen's 187 

Kumford's 186 

Wheatstone's 187 

Photometry 186 

Photophone 133 

Physics, defined 1 

Piano • 123 

Piezometer 50 

Pipes, organ 125 

Pitch 114 

Plane, inclined. . . 52 

mirrors 189 

Plates, vibrations of 23 

Plumb line. 22 

Polarization 221 

Poles of Magnets 225 

Pores 7 

Porosity 7 

Press, Bramah's 67 

Prism 198 

displacement by 198 

Propeller, screw 80 

Properties, specific 9 

universal 4 

Proof plane 236 

Psychrometer 156 

Pulley 46 

fixed 47 

movable 47 

Pulse glass 157 

Pump, air 84 

forcing 98 

suction 97 

Radiation 163 

variations of ". 166 

in vacuum. 168 

Eain 157 

bow 214 

bow secondary 215 

Kay 163 and 179 

Reaction 35 

Eeed instruments 124 

Reflection, laws 188 

Reflection, irregular 188 

regular 188 

total 196 

Refraction 194 

of air 196 

double 220 

effects..... 195 

index 195 

laws 194 

parallel faces 198 

Relay 265 

Repulsion, capillary 18 

Resistance to strain 56 

Reservoirs 76 

Resonance 113 

Resultant 36 

Roemer's discovery 182 

Rumford's photometer 186 

Safety, factor of 57 

Savart's apparatus 104 

toothed wheel 115 

Scale, musical 118 

Screw 52 

propellor 80 

Seasons, heat of 165 

Semicircular rings 264 

Semitones 119 

Shadows 183 

Simple circuit 257 

Singletouch 232 

Siphon 97 

Snell's apparatus 42 

Snow 157 

Solar microscope 211 

Solid defined 2 

Solidification 144 

Solution 144 

Sonometer 120 

Sound, defined 99 

intensity 102 

interference 110 

limits of 115 

musical 114 



Sound, reflection 109 

refraction 108 

velocity 105 

Specific gravity, determined 61 

of gases 65 

of liquids 63 

of solids 63 

Specific neat 171 

Spectroscope 212 

Spectrum 119 

colors of 199 

dark lines 213 

Spheroidal condition 158 

Spiral tube 252 

Spirit level 73 

Springs 76 

intermittent 97 

Steam boiler 175 

dome 175 

engine 173 

guage 95 

Still 154 

Strain, crushing 55 

resistance to 55 

transverse 56 

Strength of materials 54 

Strut 58 

Sublimation 148 

Suction pump 97 

Superficial expansion ... 138 

Surface defined 5 

Syren 116 

Syringe, fire 170 

Tackle 47 

Taste 11 

Telephone. . . .• 132 

Telescopes 206 

Temperature 135 

measure of 138 

Tempering 14 

musical 119 

Tenacity 10 

Terrestrial gravitation 22 

Theory defined 3 

kinetic 82 

of magnetism 228 

of music 119 

Thermo-electric pile 261 

Thermometer, filling 139 

graduation 140 

limits 141 

scales 140 

Thunder 256 

storm 253 

Tie rods..: 142 

Timbre. 114 

Tones 119 

Torricelli's experiments 90 

Torsion, elasticity of 13 

Traction, elasticity of 12 

Transparency 11 

Transverse strain 56 

Trumpets 113 

hearing 113 

speaking 113 

Tubes, speaking 113 

Tyndall's 101 

Turbine water wheel 78 

Umbra ...183 

Undershot wheel 77 

Undulatory forces 40 

Universal discharger 250 

Vacuum fountain 88 

Vaporization 147 

in vacuum 149 

Vein, contracted 74 

Vertical line 22 

Vibrations, electrical 41 

- longitudinal 41 

of membranes 128 

of plates 126 

recording of 117 

transverse 41 

Viol 123 

Voltaic electricity 256 

Volta's experiments .-. 256 



Volume, denned 5 

change of 14G 

Water, decomposed 270 

freezing by evaporation . 142 

level 73 

maximum density 143 

supply 72 

wheels. 77 

Waves, liquid 41 

Wedge 52 

Wells 76 

Wheatstone's photometer. . .187 

Wheel and axle 48 

breast 78 

overshot 78 

Savart's 115 

turbine 78 

undershot . .• 77 

Whispering gallery 112 

Wind instruments 123 

Yard 5 

Zenith 22